(2-part post):
I'll add my support to Bohne's suggestion of checking 'Time Out' for information of what's on in London.
However, I can't support the suggestion of visiting MoMI (the Museum of the Moving Image). It closed for 'refurbishment' in August, 1999 and never reopened!
I usually enjoy visiting the Photographers' Gallery (if only to try to work out how it is that some pictures which I'd throw in the bin are selling for hundreds, or even thousands, of pounds). The coffee's good too! The gallery is free and opens at 1100 daily (except Sunday, when it opens at 1200). It closes at 1800, except on Thursdays when there's late opening until 2000. The gallery is housed in two separate buildings at 5 & 8 Great Newport Street. (Travel to Leicester Square tube station. Walk up Charing Cross Road, away from Trafalgar Square, and Great Newport Street is on your right):
http://www.photonet.org.uk/index.php?latest
For a completely different style of photography, head to the National Portrait Gallery. It's at the rear of the National Gallery (i.e. near Trafalgar Square). It only gets a fraction of the visitors that its neighbouring 'big sister' does but, in my opinion, it's far more interesting. Admission is free (except to certain temporary exhibitions). It opens from 1000 to 1800 daily, with late opening until 2100 on Thursday & Friday:
http://www.npg.org.uk/live/index.asp