In America, they generally don't. It's a mild adjustment at worst. Chicago is the biggest I've seen - $98.5k base vs. $110k base for L3 SWE - but FB doesn't change their comp, Amazon and Microsoft only increase it in the SFBA and NYC (IIRC).
In fact, for new grads Amazon pays the exact same TC in Seattle and in Detroit.
I think even in finance you'll be unlikely to touch 400USD (~300 GBP) for a similar level. Sure there are outliers, but of the senior people I know in this area total comp is around 200GBP after many years. It's much easier to just contract (if you don't mind the mercenary role), you'll make similar due to the tax savings.
In fact, for new grads Amazon pays the exact same TC in Seattle and in Detroit.