Do not worry when it does not look like nice weather next weekend. Because there are so many activities and things to visit in London, where the weather would not disturb you.
Go watch a movie in the cinema is a great idea to escape the bad weather. London have got a lot of nice cinemas to go to with different services and price ranges. See below a list of the most popular cinemas in London.

Everyman Hampstead
A luxury cinema who serves wine and freshly made pizza to the seat.                    https://www.everymancinema.com/

BFI Southbank
The Cinema shows a big selection of classic and contemporary movies. The price is between £6 and £19.
https://whatson.bfi.org.uk/Online/default.asp

Statford Picturehouse
Located in east London, the cinema would never miss to show a big Blockbuster. Next to movies, they also screen Operas and Theatres live from around the world.
https://www.picturehouses.com/cinema/stratford-picturehouse

The Phoenix Cinema
With the opening in 1912, The Phoenic Cinema is one of the oldest cinemas in London. The Phoenix shows a mix of independent and foreign films.
https://phoenixcinema.co.uk/PhoenixCinema.dll/Home