I come from that neck of the woods originally and have never really managed to find the best answer for Twickenham/Richmond area visits. I have stayed at HI Kingston many times, it is far and away the best HI I've ever experienced. If you are a plat and it's a weekend night you'd stand a good chance of an upgrade to an executive room on a points stay.

The downside is if you need to drink a taxi is going to be around £20 each way. Can't be done on the train from either Kingston or Surbiton without a change, and you'd still need a cab to get to either of those stations.