Suggestion. Enter from East on the green-dotted Right of Way below the word "Works". Follow path until it turns north. Then make a left turn through the old quarry, passing south of the pools. Follow through the woods and exit through the tunnel.

The tunnel is marked as though it were an unfenced roadway.
You can see it spanning the National Trust boundaries, north of the words "Lodge Plantation".
(It looks as though it forms a crossroads with the estate entry road, but actually passes under it)