The SWR train from Wimbledon to London Waterloo takes 21 minutes. That fact changes the whole shape of a rest day — it's close enough that you're not committing to a big expedition, and far enough that you actually arrive somewhere different.
You don't need to do all of London in a day, and trying is a category error. Pick a route, go deep on it, eat somewhere worthwhile, and come back feeling like you used the time honestly.
The South Bank route (most reliable)
Walk east from Waterloo along the South Bank. River on your left the whole way, about 2km to Borough Market. The walk takes 25-30 minutes at a relaxed pace, and the detours along the way are good: Tate Modern is free and the Turbine Hall is always doing something interesting (see live rating and reviews on Google Maps); the Globe is worth a look from outside even if you're not doing a tour; Bankside generally has the quality of a city that remembers it was once a different kind of place.
The South Bank in the morning, before the tourist wave settles in around midday, is one of the better walks in London. Get out of Waterloo by 9:30am if you want the river path largely to yourself.
Borough Market is open Tuesday through Saturday. See live rating and reviews on Google Maps. If you want a guided food tour of the market, GetYourGuide has a well-reviewed option: Borough Market Food Tour. Alternatively, a London Walking Tour covers the South Bank and broader city highlights if you prefer a guided route for the whole day. It's a working market with proper specialist traders, not a food court — the fishmongers, cheese vendors, and charcuterie stalls are the real thing. Lunch from the stalls is easy and doesn't require much planning: a sandwich from Flour Power City Bakery, cheese from Neal's Yard, fruit from the market itself. If you want to sit down, Elliot's on Stoney Street grew out of the market and still uses it as a larder. Brindisa, the Spanish grocery and tapas place on the market's southern edge, is good for a quick lunch without a long queue.
After Borough Market, cross London Bridge on foot — two minutes, and the view downstream toward Tower Bridge is worth stopping for.
