This question is never really answered, but it is assumed that London gets more rain than sun. This is not actually true. One of the main reasons London is associated with bad weather is because; on several occasions people visit London only for it to rain for a whole week. This then gets talked about, and even publicized more than if the same people got a week of sunshine.
English people themselves tend to talk about the weather in London a lot. It has always seemed the norm to start talking about the weather either waiting in line at the shops, or in a queue at the bus stop. It's a way of breaking the ice. Generally British people like to converse, but the truth is London does have many good days weather too, again leading to a conversation starter.
The key to enjoying London is to plan ahead, and take into account if the weather is going to be wet, or dry. This is where disappointment sets in. When you plan for an outdoor London trip only to find it raining when you get there. Always have an alternative plan. The other thing to remember about London when it rains is that it's usually only drizzle; a light rain that can be persistent. On these rainy days instead of sitting in your London hotel room there are many places you can visit, and still enjoy a great day.
Some of the most visited places in London are the Museums. There are over 300 Museums, and Art Galleries just in London, so even if it rained all week you could not possibly visit them all. If you're in to politics, you can spend an afternoon at the houses of parliament to see how British politics actually works. The House of Commons, and the House of Lords are open to the public.
Another getaway in the rain in London is St James church. Designed by Sir Christopher Wren. There are lectures, and even concerts held in this historical building. If you want something a little different, there is always Madame Tussauds waxworks museum, which is full of lifelike famous faces you probably wouldn't mind having your photo taken with.
One of the most entertaining sights in London either in the rain, or the sun is the London Eye. This is a huge ferris wheel with a difference. Giant capsules made with glass allows all round viewing, revolving slowly, so you can take in all the sights. On a clear day you can see as far as 25 miles as the wheel reaches the top. The wheel takes a full 30 minutes to turn round one full revolution, and is a great talking point when you get back from your visit whether it's been raining, or not. The slow speed enables visitors to get on, and off without the wheel actually stopping, and there is disabled access too.