Battersea power station is almost a must see location. Although it is an upmarket shopping destination, the unique setting and reconstruction within this decommissioned power station makes it worthy of a visit for anyone. I visited on a horrible day weather wise so apart from anything else provided sanctuary on a day like this. I have yet to visit in the evening so perhaps have not yet seen the surrounding bars and restaurants in their full glory.
Natural History Museum is another refuge when the London weather turns nasty, but it is truly magnificent at any time. The building itself is breathtaking, rarely can any modern construction compete with its splendour.