No, they don't pay anything close to that. Actually, AFAIK, in Dublin the salary that Google pays for developers is on the low side of the scale (they offset that, in part, with all the benefits like free food and the rest).
Salaries do go quite up a while but statistics on the corporate ladder are stacked firmly against immigrants, the higher you go the less chance you have to find non local people.
With soft career ceiling and continuous influx of people salaries are driven down. You can still make a fine living, but nothing compared to the colleagues on the other side of the ocean.
Getting $250K is certainly doable in bank, but it does not follow a specific career plan. I have known senior system tester making 150K GBP and for the same job and responsibilities another was making 50K GBP. Doing it in 5 years out of school is difficult in tech.
It is doable without too much trouble in finance in trading, m&a, ... the trick is that you need to survive which require more luck than skills.
Overall though, in the 4.5 million workers in London, only 120K make between 100K GBP and 200K GBP, and 60K that make more than that.