diff --git a/changelog.d/8561.misc b/changelog.d/8561.misc
new file mode 100644
index 000000000..a40dedfa8
--- /dev/null
+++ b/changelog.d/8561.misc
@@ -0,0 +1 @@
+Move metric registration code down into `LruCache`.
diff --git a/synapse/api/auth.py b/synapse/api/auth.py
index 1071a0576..eb6f418b1 100644
--- a/synapse/api/auth.py
+++ b/synapse/api/auth.py
@@ -34,7 +34,6 @@ from synapse.api.room_versions import KNOWN_ROOM_VERSIONS
 from synapse.events import EventBase
 from synapse.logging import opentracing as opentracing
 from synapse.types import StateMap, UserID
-from synapse.util.caches import register_cache
 from synapse.util.caches.lrucache import LruCache
 from synapse.util.metrics import Measure
 
@@ -70,8 +69,7 @@ class Auth:
         self.store = hs.get_datastore()
         self.state = hs.get_state_handler()
 
-        self.token_cache = LruCache(10000)
-        register_cache("cache", "token_cache", self.token_cache)
+        self.token_cache = LruCache(10000, "token_cache")
 
         self._auth_blocking = AuthBlocking(self.hs)
 
diff --git a/synapse/push/push_rule_evaluator.py b/synapse/push/push_rule_evaluator.py
index 3a68ce636..4c95b149c 100644
--- a/synapse/push/push_rule_evaluator.py
+++ b/synapse/push/push_rule_evaluator.py
@@ -20,7 +20,6 @@ from typing import Any, Dict, List, Optional, Pattern, Union
 
 from synapse.events import EventBase
 from synapse.types import UserID
-from synapse.util.caches import register_cache
 from synapse.util.caches.lrucache import LruCache
 
 logger = logging.getLogger(__name__)
@@ -186,8 +185,7 @@ class PushRuleEvaluatorForEvent:
 
 
 # Caches (string, is_glob, word_boundary) -> regex for push. See _glob_matches
-regex_cache = LruCache(50000)
-register_cache("cache", "regex_push_cache", regex_cache)
+regex_cache = LruCache(50000, "regex_push_cache")
 
 
 def _glob_matches(glob: str, value: str, word_boundary: bool = False) -> bool:
diff --git a/synapse/util/caches/__init__.py b/synapse/util/caches/__init__.py
index 8fc05be27..89f0b3853 100644
--- a/synapse/util/caches/__init__.py
+++ b/synapse/util/caches/__init__.py
@@ -16,7 +16,7 @@
 
 import logging
 from sys import intern
-from typing import Callable, Dict, Optional
+from typing import Callable, Dict, Optional, Sized
 
 import attr
 from prometheus_client.core import Gauge
@@ -92,7 +92,7 @@ class CacheMetric:
 def register_cache(
     cache_type: str,
     cache_name: str,
-    cache,
+    cache: Sized,
     collect_callback: Optional[Callable] = None,
     resizable: bool = True,
     resize_callback: Optional[Callable] = None,
@@ -100,12 +100,15 @@ def register_cache(
     """Register a cache object for metric collection and resizing.
 
     Args:
-        cache_type
+        cache_type: a string indicating the "type" of the cache. This is used
+            only for deduplication so isn't too important provided it's constant.
         cache_name: name of the cache
-        cache: cache itself
+        cache: cache itself, which must implement __len__(), and may optionally implement
+             a max_size property
         collect_callback: If given, a function which is called during metric
             collection to update additional metrics.
-        resizable: Whether this cache supports being resized.
+        resizable: Whether this cache supports being resized, in which case either
+            resize_callback must be provided, or the cache must support set_max_size().
         resize_callback: A function which can be called to resize the cache.
 
     Returns:
diff --git a/synapse/util/caches/deferred_cache.py b/synapse/util/caches/deferred_cache.py
index f728cd2cf..91fdc8142 100644
--- a/synapse/util/caches/deferred_cache.py
+++ b/synapse/util/caches/deferred_cache.py
@@ -24,7 +24,6 @@ from prometheus_client import Gauge
 from twisted.internet import defer
 
 from synapse.util.async_helpers import ObservableDeferred
-from synapse.util.caches import register_cache
 from synapse.util.caches.lrucache import LruCache
 from synapse.util.caches.treecache import TreeCache, iterate_tree_cache_entry
 
@@ -54,10 +53,7 @@ class DeferredCache(Generic[KT, VT]):
 
     __slots__ = (
         "cache",
-        "name",
-        "keylen",
         "thread",
-        "metrics",
         "_pending_deferred_cache",
     )
 
@@ -89,37 +85,27 @@ class DeferredCache(Generic[KT, VT]):
             cache_type()
         )  # type: MutableMapping[KT, CacheEntry]
 
+        def metrics_cb():
+            cache_pending_metric.labels(name).set(len(self._pending_deferred_cache))
+
         # cache is used for completed results and maps to the result itself, rather than
         # a Deferred.
         self.cache = LruCache(
             max_size=max_entries,
             keylen=keylen,
+            cache_name=name,
             cache_type=cache_type,
             size_callback=(lambda d: len(d)) if iterable else None,
-            evicted_callback=self._on_evicted,
+            metrics_collection_callback=metrics_cb,
             apply_cache_factor_from_config=apply_cache_factor_from_config,
         )
 
-        self.name = name
-        self.keylen = keylen
         self.thread = None  # type: Optional[threading.Thread]
-        self.metrics = register_cache(
-            "cache",
-            name,
-            self.cache,
-            collect_callback=self._metrics_collection_callback,
-        )
 
     @property
     def max_entries(self):
         return self.cache.max_size
 
-    def _on_evicted(self, evicted_count):
-        self.metrics.inc_evictions(evicted_count)
-
-    def _metrics_collection_callback(self):
-        cache_pending_metric.labels(self.name).set(len(self._pending_deferred_cache))
-
     def check_thread(self):
         expected_thread = self.thread
         if expected_thread is None:
@@ -154,21 +140,18 @@ class DeferredCache(Generic[KT, VT]):
         if val is not _Sentinel.sentinel:
             val.callbacks.update(callbacks)
             if update_metrics:
-                self.metrics.inc_hits()
+                m = self.cache.metrics
+                assert m  # we always have a name, so should always have metrics
+                m.inc_hits()
             return val.deferred
 
-        val = self.cache.get(key, _Sentinel.sentinel, callbacks=callbacks)
-        if val is not _Sentinel.sentinel:
-            self.metrics.inc_hits()
-            return val
-
-        if update_metrics:
-            self.metrics.inc_misses()
-
-        if default is _Sentinel.sentinel:
+        val = self.cache.get(
+            key, default, callbacks=callbacks, update_metrics=update_metrics
+        )
+        if val is _Sentinel.sentinel:
             raise KeyError()
         else:
-            return default
+            return val
 
     def set(
         self,
diff --git a/synapse/util/caches/dictionary_cache.py b/synapse/util/caches/dictionary_cache.py
index 8592b9368..8b426c005 100644
--- a/synapse/util/caches/dictionary_cache.py
+++ b/synapse/util/caches/dictionary_cache.py
@@ -19,8 +19,6 @@ from collections import namedtuple
 
 from synapse.util.caches.lrucache import LruCache
 
-from . import register_cache
-
 logger = logging.getLogger(__name__)
 
 
@@ -46,18 +44,16 @@ class DictionaryCache:
     """
 
     def __init__(self, name, max_entries=1000):
-        self.cache = LruCache(max_size=max_entries, size_callback=len)
+        self.cache = LruCache(max_size=max_entries, cache_name=name, size_callback=len)
 
         self.name = name
         self.sequence = 0
         self.thread = None
-        # caches_by_name[name] = self.cache
 
         class Sentinel:
             __slots__ = []
 
         self.sentinel = Sentinel()
-        self.metrics = register_cache("dictionary", name, self.cache)
 
     def check_thread(self):
         expected_thread = self.thread
@@ -82,8 +78,6 @@ class DictionaryCache:
         """
         entry = self.cache.get(key, self.sentinel)
         if entry is not self.sentinel:
-            self.metrics.inc_hits()
-
             if dict_keys is None:
                 return DictionaryEntry(
                     entry.full, entry.known_absent, dict(entry.value)
@@ -95,7 +89,6 @@ class DictionaryCache:
                     {k: entry.value[k] for k in dict_keys if k in entry.value},
                 )
 
-        self.metrics.inc_misses()
         return DictionaryEntry(False, set(), {})
 
     def invalidate(self, key):
diff --git a/synapse/util/caches/lrucache.py b/synapse/util/caches/lrucache.py
index 33eae2b7c..e4804f79e 100644
--- a/synapse/util/caches/lrucache.py
+++ b/synapse/util/caches/lrucache.py
@@ -18,6 +18,7 @@ from functools import wraps
 from typing import Callable, Optional, Type, Union
 
 from synapse.config import cache as cache_config
+from synapse.util.caches import CacheMetric, register_cache
 from synapse.util.caches.treecache import TreeCache
 
 
@@ -43,27 +44,29 @@ class _Node:
 
 class LruCache:
     """
-    Least-recently-used cache.
+    Least-recently-used cache, supporting prometheus metrics and invalidation callbacks.
+
     Supports del_multi only if cache_type=TreeCache
     If cache_type=TreeCache, all keys must be tuples.
-
-    Can also set callbacks on objects when getting/setting which are fired
-    when that key gets invalidated/evicted.
     """
 
     def __init__(
         self,
         max_size: int,
+        cache_name: Optional[str] = None,
         keylen: int = 1,
         cache_type: Type[Union[dict, TreeCache]] = dict,
         size_callback: Optional[Callable] = None,
-        evicted_callback: Optional[Callable] = None,
+        metrics_collection_callback: Optional[Callable[[], None]] = None,
         apply_cache_factor_from_config: bool = True,
     ):
         """
         Args:
             max_size: The maximum amount of entries the cache can hold
 
+            cache_name: The name of this cache, for the prometheus metrics. If unset,
+                no metrics will be reported on this cache.
+
             keylen: The length of the tuple used as the cache key. Ignored unless
                 cache_type is `TreeCache`.
 
@@ -73,9 +76,13 @@ class LruCache:
 
             size_callback (func(V) -> int | None):
 
-            evicted_callback (func(int)|None):
-                if not None, called on eviction with the size of the evicted
-                entry
+            metrics_collection_callback:
+                metrics collection callback. This is called early in the metrics
+                collection process, before any of the metrics registered with the
+                prometheus Registry are collected, so can be used to update any dynamic
+                metrics.
+
+                Ignored if cache_name is None.
 
             apply_cache_factor_from_config (bool): If true, `max_size` will be
                 multiplied by a cache factor derived from the homeserver config
@@ -94,6 +101,19 @@ class LruCache:
         else:
             self.max_size = int(max_size)
 
+        if cache_name is not None:
+            metrics = register_cache(
+                "lru_cache",
+                cache_name,
+                self,
+                collect_callback=metrics_collection_callback,
+            )  # type: Optional[CacheMetric]
+        else:
+            metrics = None
+
+        # this is exposed for access from outside this class
+        self.metrics = metrics
+
         list_root = _Node(None, None, None, None)
         list_root.next_node = list_root
         list_root.prev_node = list_root
@@ -105,8 +125,8 @@ class LruCache:
                 todelete = list_root.prev_node
                 evicted_len = delete_node(todelete)
                 cache.pop(todelete.key, None)
-                if evicted_callback:
-                    evicted_callback(evicted_len)
+                if metrics:
+                    metrics.inc_evictions(evicted_len)
 
         def synchronized(f):
             @wraps(f)
@@ -169,13 +189,17 @@ class LruCache:
             return deleted_len
 
         @synchronized
-        def cache_get(key, default=None, callbacks=[]):
+        def cache_get(key, default=None, callbacks=[], update_metrics=True):
             node = cache.get(key, None)
             if node is not None:
                 move_node_to_front(node)
                 node.callbacks.update(callbacks)
+                if update_metrics and metrics:
+                    metrics.inc_hits()
                 return node.value
             else:
+                if update_metrics and metrics:
+                    metrics.inc_misses()
                 return default
 
         @synchronized
diff --git a/tests/util/test_lrucache.py b/tests/util/test_lrucache.py
index 0adb2174a..f12834eda 100644
--- a/tests/util/test_lrucache.py
+++ b/tests/util/test_lrucache.py
@@ -59,7 +59,7 @@ class LruCacheTestCase(unittest.HomeserverTestCase):
         self.assertEquals(cache.pop("key"), None)
 
     def test_del_multi(self):
-        cache = LruCache(4, 2, cache_type=TreeCache)
+        cache = LruCache(4, keylen=2, cache_type=TreeCache)
         cache[("animal", "cat")] = "mew"
         cache[("animal", "dog")] = "woof"
         cache[("vehicles", "car")] = "vroom"
@@ -160,7 +160,7 @@ class LruCacheCallbacksTestCase(unittest.HomeserverTestCase):
         m2 = Mock()
         m3 = Mock()
         m4 = Mock()
-        cache = LruCache(4, 2, cache_type=TreeCache)
+        cache = LruCache(4, keylen=2, cache_type=TreeCache)
 
         cache.set(("a", "1"), "value", callbacks=[m1])
         cache.set(("a", "2"), "value", callbacks=[m2])