It's one of my missions to correct this falacy. The number of days with rain in London is just around average and the overall precipitation is quite low.
Here's an example with data comparing London and Lisbon (which people usually believe is always sunny):
Check out the mean sunshine hours in those tables to figure out why Lisbon is perceived to always be sunny, it is because it is. Literally twice the sunny hours a year.
There is a pretty big difference between 12 hours of cloud and drizzle and 2 hours of steady rain followed by 10 of sunshine in terms of the human misery factor.
While I understand your point, my experience doesn't really follow that logic (I have lived in Lisbon for 25 years and I'm on my third year in London). In my experience, while it's usually sunshine, when it rains in Lisbon it does rain most of the day and it's usually not drizzle but heavy rain (which I believe is the reason why precipitation is so high in volume in Lisbon; Oporto is even worse) while in London it can drizzle every day for a couple of minutes and then stop and "clear" (clear London style, meaning less clouds) and then drizzle again hours later. I assume London's sky is more chaotic because we're in an island in the middle of the sea but I'm no expert on the matter.
I usually say my Portuguese friends about London: "It doesn't rain a lot but it rains every day. Thing is, by Lisbon standards we would never call this rain." :)
Another curiosity is how tough the winter is in both cities. In London it's the greyness and lack of sunlight for months and months. In Lisbon it's the heavy rains. I spent this last winter in Lisbon and it was most probably one of the winters with more precipitation. Humans exagerate, I know that, but it really felt like it (heavy) rained for almost six months. It stopped a few weeks ago, sunny Lisbon is back again at full throttle!
I used to live on the other side of the lake from Seattle, and there too the winters were worse for the "greyness and lack of sunlight for months and months" than for the rain.
Usually enough that I'd still rather cab a mile than walk it. (I couldn't afford cabs then.)
It rains less now that the gulf stream is shifting. It's going to get a lot colder, though.
Edit: well according to http://www.bbc.co.uk/climate/impact/gulf_stream.shtml "This slowing will have a cooling effect but the temperature will still increase in the region overall" due to the global warming effect.
