> winter is cold, rainy, and grey

If you're comparing a British winter to a southern hemisphere "winter", sure it's not a great place to be. But for the mostpart, London is actually pretty good for it's winter. Yes you occasionaly get snow which is great for a day or two and then it turns to slush and ice and ends up being annoying, but really London is mild compared to the rest of the UK.

It is a big adjustment going from a southern hemisphere country to northern, so I don't blame you if you can't take it, but really it's not that bad here.