All the museums on Exhibition Road, South Ken. are worth visiting, The Natural History, Victoria & Albert, and Science Museum.
I've not been since the 1980's, but I went to a seriously shit secondary school and ended up bunking off every day and spending all my time at the museums instead. I learn't far more back then than being in a shit school. The Science Museum was my favourite. After a few months of this I eventually switched to a proper school that I actually enjoyed going to each day and my inner 11 year old museum curator decided to retire, and give comprehensive school education another stab.