That's averages over the whole countries though - the north and west of the UK (particularly the Scottish Highlands and the Lake District) are a lot wetter than the south-east where London is.
Also, "volume of rain" might be misleading because it doesn't give you a feeling for how often it rains. The Highlands in particular can have a light rain that falls for weeks at a time (or at least seems like it if you are in a tent).
Most of the Bay Area gets about the same amount of rain as London. The key difference is that in Cupertino/Los Gators/Palo Alto it rains less often but with more intensity.
Not just a raincoat, I've had snow, sunny summer, storm gusts, hail and rain on the same day just this week, I'm int he SW though not entirely west.
I remember one time a few years back when I lived in Stavanger, I went to the post office in the city center there in a bright nice summer day and came out to torrential rain and rivers in the street!