--- a
+++ b/tests/docker/test_drivers.py
@@ -0,0 +1,26 @@
+import pytest
+
+
+def test_driver_in_container(call_cli_docker, engine):
+    # This test doesn't make sense for these in-memory databases
+    if engine.name in {"in_memory", "sqlite"}:
+        pytest.skip()
+
+    backends = {
+        "mssql": "ehrql.backends.tpp.TPPBackend",
+        "trino": "ehrql.backends.emis.EMISBackend",
+    }
+
+    if engine.name not in backends:
+        assert False, f"no backend for database: {engine.name}"
+
+    backend = backends[engine.name]
+    url = engine.database.container_url()
+
+    call_cli_docker(
+        "test-connection",
+        "--backend",
+        backend,
+        "--url",
+        url,
+    )