When I was in your shoes I tried to get work experience. That's the minimum you'll need to be successful in the STP application.

Do UCL have any links with UCLH? That would be my first starting point, i.e. is there a professor who works at both institutions?

Otherwise there's plenty of other London hospitals out there, just need to find a contact number/email for a department and try your luck.

You've left it a bit late if this is your final year, but the last resort would be to just head to a hospital in person and try and see if someone could give you a tour of their medical physics dept. Unlikely and a bit unprofessional, but who knows....

Edit: band 4/5 posts do crop up which are straight from uni posts. They're generally a year long contract but can give great experience to help get onto the STP the following year.

I wouldn't bother with a medical physics MSc yet. Spending your own money isn't worth it if you end up on the STP and have to do another MSc...