Museum jobs are not a dime-a-dozen. (Or whatever the Brit version of that is.) And you are up against people who have in-country credentials, which you do not (I don't think). So unless, and I don't mean to be harsh, you have something extra-special to offer the employers, or have the right connections, you'll be very fortunate indeed to get anything above a part-time docent job if you have to go to work immediately. If you took one of those entry-level jobs, you might be later able to work it into something more substantial. You may have to be willing to accept anything, anywhere, to get a foot in the door.
So, at present, although London seems promising, you really don't have a clue where it is you'd find a job in your field. It may not be London. So moving closer to London for only a six month stint is not what I'd do. I'd sign for the six month extension where you will already have a place to call home. Land there, get settled in, and then take the lay of the land. My guess is that it will take that long, at a minimum, for you to sort out your actual career opportunities in the UK - you may find yourself having to apply for positions a long way from London.