diff --git a/.ci/scripts/test_old_deps.sh b/.ci/scripts/prepare_old_deps.sh
similarity index 71%
rename from .ci/scripts/test_old_deps.sh
rename to .ci/scripts/prepare_old_deps.sh
index 478c8d639ae8..7e4f060b17b8 100755
--- a/.ci/scripts/test_old_deps.sh
+++ b/.ci/scripts/prepare_old_deps.sh
@@ -5,18 +5,8 @@
 # - creates a venv with these old versions using poetry; and finally
 # - invokes `trial` to run the tests with old deps.
 
-# Prevent tzdata from asking for user input
-export DEBIAN_FRONTEND=noninteractive
-
 set -ex
 
-apt-get update
-apt-get install -y \
-        python3 python3-dev python3-pip python3-venv pipx \
-        libxml2-dev libxslt-dev xmlsec1 zlib1g-dev libjpeg-dev libwebp-dev
-
-export LANG="C.UTF-8"
-
 # Prevent virtualenv from auto-updating pip to an incompatible version
 export VIRTUALENV_NO_DOWNLOAD=1
 
@@ -33,12 +23,6 @@ export VIRTUALENV_NO_DOWNLOAD=1
 #   a `cryptography` compiled against OpenSSL 1.1.
 # - Omit systemd: we're not logging to journal here.
 
-# TODO: also replace caret bounds, see https://python-poetry.org/docs/dependency-specification/#version-constraints
-# We don't use these yet, but IIRC they are the default bound used when you `poetry add`.
-# The sed expression 's/\^/==/g' ought to do the trick. But it would also change
-# `python = "^3.7"` to `python = "==3.7", which would mean we fail because olddeps
-# runs on 3.8 (#12343).
-
 sed -i \
    -e "s/[~>]=/==/g" \
    -e '/^python = "^/!s/\^/==/g' \
@@ -55,7 +39,7 @@ sed -i \
 # toml file. This means we don't have to ensure compatibility between old deps and
 # dev tools.
 
-pip install --user toml
+pip install toml wheel
 
 REMOVE_DEV_DEPENDENCIES="
 import toml
@@ -69,8 +53,8 @@ with open('pyproject.toml', 'w') as f:
 "
 python3 -c "$REMOVE_DEV_DEPENDENCIES"
 
-pipx install poetry==1.1.14
-~/.local/bin/poetry lock
+pip install poetry==1.2.0
+poetry lock
 
 echo "::group::Patched pyproject.toml"
 cat pyproject.toml
@@ -78,6 +62,3 @@ echo "::endgroup::"
 echo "::group::Lockfile after patch"
 cat poetry.lock
 echo "::endgroup::"
-
-~/.local/bin/poetry install -E "all test"
-~/.local/bin/poetry run trial --jobs=2 tests
diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 720cb13907fd..601ec63bf454 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -150,16 +150,47 @@ jobs:
     # Note: sqlite only; no postgres
     if: ${{ !cancelled() && !failure() }} # Allow previous steps to be skipped, but not fail
     needs: linting-done
-    runs-on: ubuntu-latest
+    runs-on: ubuntu-20.04
     steps:
       - uses: actions/checkout@v2
-      - name: Test with old deps
-        uses: docker://ubuntu:focal # For old python and sqlite
-        # Note: focal seems to be using 3.8, but the oldest is 3.7?
-        # See https://github.com/matrix-org/synapse/issues/12343
+
+      # There aren't wheels for some of the older deps, so we need to install
+      # their build dependencies
+      - run: |
+          sudo apt-get -qq install build-essential libffi-dev python-dev \
+          libxml2-dev libxslt-dev xmlsec1 zlib1g-dev libjpeg-dev libwebp-dev
+
+      - uses: actions/setup-python@v4
+        with:
+          python-version: '3.7'
+
+      # Calculating the old-deps actually takes a bunch of time, so we cache the
+      # pyproject.toml / poetry.lock. We need to cache pyproject.toml as
+      # otherwise the `poetry install` step will error due to the poetry.lock
+      # file being outdated.
+      #
+      # This caches the output of `Prepare old deps`, which should generate the
+      # same `pyproject.toml` and `poetry.lock` for a given `pyproject.toml` input.
+      - uses: actions/cache@v3
+        id: cache-poetry-old-deps
+        name: Cache poetry.lock
         with:
-          workdir: /github/workspace
-          entrypoint: .ci/scripts/test_old_deps.sh
+          path: |
+            poetry.lock
+            pyproject.toml
+          key: poetry-old-deps2-${{ hashFiles('pyproject.toml') }}
+      - name: Prepare old deps
+        if: steps.cache-poetry-old-deps.outputs.cache-hit != 'true'
+        run: .ci/scripts/prepare_old_deps.sh
+
+      # We only now install poetry so that `setup-python-poetry` caches the
+      # right poetry.lock's dependencies.
+      - uses: matrix-org/setup-python-poetry@v1
+        with:
+          python-version: '3.7'
+          extras: "all test"
+
+      - run: poetry run trial -j 2 tests
       - name: Dump logs
         # Logs are most useful when the command fails, always include them.
         if: ${{ always() }}
diff --git a/changelog.d/13707.misc b/changelog.d/13707.misc
new file mode 100644
index 000000000000..e72c322d2e28
--- /dev/null
+++ b/changelog.d/13707.misc
@@ -0,0 +1 @@
+Update trial old deps CI to use poetry 1.2.0.