Where I live now, in China, I don't carry an umbrella. When it rains, it pours. For ages. So an umbrella is little help.
In London, rain is much lighter, but much more frequent and much less predictable. So carrying an umbrella is a must.
I forgot this on my last trip to London. It was sunny when I got on the underground at Heathrow. By the time I got to central London, it was pouring, and I was soaked by the time I had walked to the office.
I mean it rains a bit but reputation for rain is far in excess of the reality if you were to compare it with many north American cities.
Have a look at http://www.worldclimate.com/ to compare. London is pretty dry.