I'm in a similar position to you. You may be able to get an employer to pay for the top-up modules if you apply to a trainee biomedical scientist position. To do this though you will need to get your degree assessed by the Institute of Biomedical Science to show which modules you need to take to 'top up' your degree to one which meets their standards.
Unfortunately this assessment costs £250. If you look on their website (IBMS.org), it's tricky to find but you are looking for the application form called 'Form B'. They will assess your degree to see if it meets their standards to practise as a biomedical scientist (which it won't) and then they send you a letter which tells you what top-up modules you need to take and what universities offer them.
When you apply for trainee biomedical scientist positions it may be enough to provide this letter which shows you are allowed to register as a biomedical scientist providing you complete the on-the job training and some top-up modules which the employer would let you take time out of work to do and they will probably pay for.
OR there is a distance-learning course at Ulster University which is 1 year long and you can do at the same time as working in whatever job you're doing now to finance yourself, which is designed to top-up your degree to a IBMS standard. Link here:
http://prospectus.ulster.ac.uk/course/?id=9151. This is a good option for you at the moment as then you'd already be of the academic standard required when you apply to jobs which will put you in a better position. You still need to get your degree assessed though, that's necessary for registration with the IBMS which you need in order to work. I know on the Ulster webpage it says that you'd normally need to be employed in a related job to start the course, however I know someone who was unemployed when they started it so it doesn't seem to be a strict rule.
Hope that all makes some sense, I'm only just getting to grips with it myself.
Edit: sorry there are probably other courses than just the one at ulster uni but that's one which I know of