My friends and friends of friends frequently ask me what to see in London if you visit it just for a weekend or you have to fly through London and you have a day. My advice would be: do the same thing what you would do in any other European capital. Take a sightseeing bus. The ticket will give you both a bus tour and a river cruise. The river tour is fantastic in London. The Thames is wide, fast and you have plenty of sightseeing opportunities unlike in other European capitals.
The bus tour will give you a fantastic overview of London's iconic sites.
As for museums, V&A is an absolute favourite among most tourist however Tate Modern is the most visited museum in the whole world. Tate Modern has a fantastic marketing team which "made" the museum famous however the modern art is not for all so behave and check what is going on at the museum while you are in town. Currently its Matisse and Malevich along with Tate's collection. As to V&A its conveniently located next to Science and Natural History Museums, Knightsbridge, Hyde Park and South Kensington which gives you an opportunity to walk around and explore the affluent neighbourhood, one of the most famous parks in the world and potentially a Kensington palace.
British Museum is probably number two in my personal list of historical museums after the V&A. Its website has a fantastic guidance "if you've got 1 hour for British museum", 3 hours etc
In case you have great stamina go to one of the iconic musicals like Phantom of the Opera.
That's about it what you can do in London in 2 days - take a bus tour, a river cruise, a view from the Shard or Tower 42, a little bit of museum experience and a pint.