Well, the 1 bedroom in London is far from 3000-4000 per month.
I don't know the details of the costs of living and all the expenses. Maybe SV is better but I just want to say that it is not twice as better, contrary to what some comments would have you think.
The cost of living in SF is 1.4 times higher but the wage is 1.75 times higher. Note this number is assuming you are renting, and not considering electronics which is a lot cheaper in the US.
The house price in London is still more expensive, and if you are a senior developer in your 30s that's probably more relevant than renting price.
Factor those in, as a software developer, in SV you are easily 30-50% better off than London, the best paid city in Europe. The pay gap between Europe and US do exist, Silicon Valley is the technology centre of the world, Europe isn't.
I don't know the details of the costs of living and all the expenses. Maybe SV is better but I just want to say that it is not twice as better, contrary to what some comments would have you think.