I stand corrected. Only paid Envoy passengers get the comp transportation. I'm note sure if they still do this post 9/11.
If you are in London for only 5 days or less here's a special ($20 roundtrip) on the Gatwick Express. I don't know if you can purchase it there - the mailing charges are high.
http://raileurope.lycos.com/us/rail/...ck_express.htm