OP, I won't address the issue of escorting as you have had some great advice. You do sound very vulnerable though and I think for that reason, please treat yourself kindly.
I completely believe people can fall through the net in this day and age. It is very easy to not fit into any of the criteria for help (e.g. disability) but be too ill to work f/t or in certain jobs. I have a relative like this and he also experiences so much anxiety about money and this does not help MH problems at all.
One solution you may not have thought of, which definitely would bring in a bit of extra money if not the whole amount you need is tutoring- if you have two degrees, register with every tutoring agency going, call them and see if you can take classes. Usually they prefer it if you go to the clients, but be careful you don't spend much money on travel (or get a travelcard in London so there is a limit on this). You can offer a range of subjects, not just your degree ones, but anything you took at A-level.
You won't get £50 a time (!), but you might get £25-30 an hour with a small cut for the agency and people sometimes do 1.30 or 2 hour sessions. You could set up on your own but this requires advertising- unless you know people at a local school/access to parents.
If you are well-educated this can be a good solution, however I think it is not possible to earn a long-term full wage doing this unless you really do it as a full-time job (so two or three clients every day). You may then be able to get the benefit where you get a minimum amount of money and are assumed to be working more than 16 or 21 hours a week- my relative does this and he often doesn't work that much (due to illness) but gets housing benefit and just enough money to get by food-wise.
One thing you might need to think flexibly about, and I hear you don't want to, is housing costs if you can't get full housing benefit for that rental. There ARE cheaper rooms in London in shared houses, and that is one very obvious way to shave a reasonable amount off your living costs. A live-in position, doing some care work (limited perhaps by your back) is another.
Good luck, now you have calmed down, I think you have more options than you think.