diff --git a/changelog.d/13798.misc b/changelog.d/13798.misc
new file mode 100644
index 000000000000..e4ec2d77d666
--- /dev/null
+++ b/changelog.d/13798.misc
@@ -0,0 +1 @@
+Fix a memory leak when running the unit tests.
\ No newline at end of file
diff --git a/synapse/util/caches/__init__.py b/synapse/util/caches/__init__.py
index 35c0be08b01d..f7c3a6794ed0 100644
--- a/synapse/util/caches/__init__.py
+++ b/synapse/util/caches/__init__.py
@@ -205,8 +205,9 @@ def register_cache(
         add_resizable_cache(cache_name, resize_callback)
 
     metric = CacheMetric(cache, cache_type, cache_name, collect_callback)
+    metric_name = "cache_%s_%s" % (cache_type, cache_name)
     caches_by_name[cache_name] = cache
-    CACHE_METRIC_REGISTRY.register_hook(metric.collect)
+    CACHE_METRIC_REGISTRY.register_hook(metric_name, metric.collect)
     return metric
 
 
diff --git a/synapse/util/metrics.py b/synapse/util/metrics.py
index 9687120ebfdb..165480bdbef7 100644
--- a/synapse/util/metrics.py
+++ b/synapse/util/metrics.py
@@ -15,7 +15,7 @@
 import logging
 from functools import wraps
 from types import TracebackType
-from typing import Awaitable, Callable, Generator, List, Optional, Type, TypeVar
+from typing import Awaitable, Callable, Dict, Generator, Optional, Type, TypeVar
 
 from prometheus_client import CollectorRegistry, Counter, Metric
 from typing_extensions import Concatenate, ParamSpec, Protocol
@@ -220,21 +220,21 @@ class DynamicCollectorRegistry(CollectorRegistry):
 
     def __init__(self) -> None:
         super().__init__()
-        self._pre_update_hooks: List[Callable[[], None]] = []
+        self._pre_update_hooks: Dict[str, Callable[[], None]] = {}
 
     def collect(self) -> Generator[Metric, None, None]:
         """
         Collects metrics, calling pre-update hooks first.
         """
 
-        for pre_update_hook in self._pre_update_hooks:
+        for pre_update_hook in self._pre_update_hooks.values():
             pre_update_hook()
 
         yield from super().collect()
 
-    def register_hook(self, hook: Callable[[], None]) -> None:
+    def register_hook(self, metric_name: str, hook: Callable[[], None]) -> None:
         """
         Registers a hook that is called before metric collection.
         """
 
-        self._pre_update_hooks.append(hook)
+        self._pre_update_hooks[metric_name] = hook