There is enough to keep you busy every day for at least a month. It's a mistake to think that London is all history and art, though. There are plenty of other things to do. And after you've done all this, you've still only scratched the surface of London. Any time is good to visit London.
Summer is the most pleasant time, but also the most crowded.
The history of London is woven into its architecture. Even individual streets in London are worthy of a visit. The neoclassical British Museum is one of the world's greatest. The have a range of exhibits, including two Magna Cartas, the Rosetta stone, the Elgin Marbles, Egyptian mummies, and half the treasures of the ancient world. Art lovers will want to explore the Tate Gallery, the National Gallery, and the National Portrait Gallery.