Route 11 is the best sightseeing bus nobody talks about. Liverpool street to chelsea via bank, st paul's, fleet street, strand, westminster, sloane square. Upper deck, right side for optimal views.

Standard bus fare vs £30+ for hop-on-hop-off nonsense. Takes 50-70 minutes end to end depending on traffic. Board at liverpool street, grab upstairs front right seat. You'll see the city, cross waterloo bridge with river views, pass westminster abbey.