If I could switch companies easily I would. But you need to be insanely good at math/statistics to pass the interviews, which I'm not, and you need to show enthusiasm for the role, which is difficult.
Can you try to get into the hiring committee at your current employer? You'll get some free practice.
Then the past few months I've had several other big tech companies reach out and told them I'm not going to interview this summer.
I recently had a former Microsoft Program Manager tell me that "the more experienced the person being interviewed the worse they are at interviews because that haven't used that part the brain in 20 years".
The interviews are such a pain now make me kind of wish I was doing something other than Computer Science.
(I don't know OP personally and I'm not commenting on them specifically, they could be amazing)
I would say that your first concern is to find something that you actually want to do. When you leave to get away from a job you will probably end up in the same space and the cycle will start again
The money you get paid to work in London is in part because how expensive London is, so moving home with a pay cut may actually see you better off
Be careful of how this will affect your relationship. You don't want to get to the point where the line "I put up with is this shit for your career" leaves your mouth
Sports data (odds and pricing) is another area that ML could get you a job