Hi Lauren,
That’s opened a can of worms, so to speak. I’ve tried a few ticket selling sites, most of which didn’t want to sell me the correct ticket. The one which did work was southeasternrailway.co.uk, but that points out that it’s cheaper to go all the way to Waterloo and change onto the Underground there. Perversely you pay more for each zone that you want to use the Underground. So the fare is now £16.50 with the railcard. You can put Sloane Square in as the destination on Southeastern, but the ticket will be to Zone U1 London and can be used to go to any zone 1 tube station from either Vauxhall or Waterloo.
I did try South Western Railway’s website, but they wanted to charge singles each way, which hit the £12 minimum fare in the morning and was thus more expensive. Another site didn’t seem to understand what I wanted and was only selling tickets to Vauxhall.
You can also try buying the tickets at a ticket office, but make sure that the route is “via Surbiton” rather than “Any Permitted” which allows you to go via Virginia Water.