Places like Silicon Valley and Seattle are still outliers but if you looked at "typical" software engineering salaries in the US the differences in salaries are explainable almost entirely by differences in payroll costs (various taxes, regulations, etc) that the employee never sees.
In short, the apparent arbitrage opportunity doesn’t actually exist. As you would expect in any semi-liquid, semi-efficient market.
Salaries in London are certainly higher than the rest of the country (by a comfortable margin), but anywhere from £40-80k seems to be the norm. £80k being at the high end of senior. Six figures is possible, but fairly unlikely outside of finance or senior positions at the megacorps. If you don't live in London (or the South East), £40k alone would be considered a very comfortable salary.
This is corroborated by Glassdoor, various sites which claim to have surveyed salaries and actual job adverts (e.g. via StackOverflow Jobs or recruiters).
It is ill advised to ignore finance, big companies, and contracting.
Contracting, though, yeah. 500 a day for a competent but unexceptional Java developer? 800 for Scala? More if you happen to know whatever's hot right now? A contractor friend once told me to plan around billing 220 days a year, which would see the Java grunt on 110k, and the Scala astronaut on 176k.
One interesting thing in London is many (most?) permanent roles have a two or even three month contractual "notice period". So if you hand in your notice, you're stuck working for another three months. This causes friction in the labor market which certainly has a depressive effect on wages.
I'm also not all that bothered about it. I've never decided to quit a job and needed to be out one month later - i am not the sort of person who bumps into someone founding a hot new startup and decides to jump on board. Four and a half months sounds like about the amount of time it would take me to find a new job anyway!
[1] https://en.wikipedia.org/wiki/Best_alternative_to_a_negotiat...
>>> I've never decided to quit a job and needed to be out one month later
It's a big hassle to get a new job if you can't be available before a few months. I personally had the case that a new job was terrible and left rather quickly. That would have been a problem if there were multiple months of notice.