diff --git a/.github/actions/docker-clean/action.yaml b/.github/actions/docker-clean/action.yaml
index 56bf2f88ab..107df9a7e5 100644
--- a/.github/actions/docker-clean/action.yaml
+++ b/.github/actions/docker-clean/action.yaml
@@ -1,5 +1,5 @@
 name: Docker cleanup action
-description: Composite action for removing Docker images
+description: Composite action for removing Docker containers and images
 author: "Devito"
 
 inputs:
@@ -10,12 +10,28 @@ inputs:
   tag:
     description: "Tag of the built image to use"
     required: true
+  name:
+    description: "Name substring used by the docker-run action"
+    default: ""
 
 runs:
   using: "composite"
   steps:
     - id: dockerclean
-      name: "Cleanup docker image"
+      name: "Cleanup Docker resources"
       shell: bash
+      env:
+        NAME: ${{ inputs.name }}
+        TAG: ${{ inputs.tag }}
+        UNIQUE: ${{ inputs.uid }}
       run: |
-          docker image rm -f "${{ inputs.tag }}_${{ inputs.uid }}"
+        CONTAINER_NAME="ci-${NAME:-${TAG}}-${UNIQUE}"
+        CID_FILE="${RUNNER_TEMP}/${CONTAINER_NAME}.cid"
+
+        if [[ -s "${CID_FILE}" ]]; then
+          CONTAINER_ID=$(< "${CID_FILE}")
+          docker container rm -f "${CONTAINER_ID}" 2>/dev/null || true
+        fi
+        rm -f "${CID_FILE}"
+
+        docker image rm -f "${TAG}_${UNIQUE}"
diff --git a/.github/actions/docker-run/action.yaml b/.github/actions/docker-run/action.yaml
index 375a21c7ce..60f7b43325 100644
--- a/.github/actions/docker-run/action.yaml
+++ b/.github/actions/docker-run/action.yaml
@@ -50,12 +50,20 @@ runs:
       shell: bash
       env:
         NAME: ${{ inputs.name }}
+        TAG: ${{ inputs.tag }}
+        UNIQUE: ${{ inputs.uid }}
       run: |
+        CONTAINER_NAME="ci-${NAME:-${TAG}}-${UNIQUE}"
+        CID_FILE="${RUNNER_TEMP}/${CONTAINER_NAME}.cid"
+
+        rm -f "${CID_FILE}"
+
         docker run \
           --init -t --rm \
           ${{ inputs.args }} \
-          --name "ci-${NAME:-${{ inputs.tag }}}-${{ inputs.uid }}" \
+          --name "${CONTAINER_NAME}" \
+          --cidfile "${CID_FILE}" \
           --env-file=docker/coverage.env \
           ${{ steps.processenv.outputs.docker_environment_args }} \
-          "${{ inputs.tag }}_${{ inputs.uid }}" \
+          "${TAG}_${UNIQUE}" \
           ${{ inputs.command }}
diff --git a/.github/actions/readme.md b/.github/actions/readme.md
index d6f249963d..93d0d1766b 100644
--- a/.github/actions/readme.md
+++ b/.github/actions/readme.md
@@ -56,6 +56,7 @@ Inputs:
 - The tag must match built image, easily obtained from build action
 - If you provide a custom name `foo` the container name will be `ci-foo-UUUUUUUUUU` where UUUUUUUUUU is the UID
 - The default args `--init -t --rm` are _always_ added
+- The latest container ID is stored under `RUNNER_TEMP` for the docker-clean action
 - Environment variables must be passed a single environment variable per line, best achieved with the (`|`) syntax in yaml
 - Only a single command is executed, not a list of commands. Using `;` or `&&` will result in subsequent commands being executed outside of the docker environment
 
@@ -87,12 +88,16 @@ Inputs:
 
 - `uid`: Unique identifier output from docker-build action
 - `tag`: Tag of the built image to use
+- `name`: Name substring passed to docker-run (optional)
 
 ### Notes
 
 - UID must be unique, easily obtained from build action
 - Tag must match built image, easily obtained from build action
-- Use `if: always()` to always clean up the image, even if the workflow fails
+- If set, name must match the optional name passed to docker-run
+- The container is force-removed using the ID recorded by docker-run
+- Use `if: always()` to clean up the container and image even if the workflow
+  fails
 
 Example:
 
@@ -100,7 +105,7 @@ Example:
 jobs:
   test:
     steps:
-    - name: Cleanup Docker image
+    - name: Cleanup Docker resources
       if: always()
       uses: ./.github/actions/docker-clean
       with: