In December my wife I had a 22-hour stopover. We overnighted for about $70 (including BF), took the Tube to Covenant Gardens, walked through Christmas markets, by Trafalgar Square / 10 Downing / Big Ben / Parliament / Westminster Abbey and returned from Hyde Park (both stops no connections, some of which are outside and cold in December). This took about 5 hours total. The British Museum is free, but we did that a few years ago.
Sounds like he Khant handle it.