You could do a course in Health & Social Care.
I've just completed an OCR National Diploma in Health & Social Care at college. It took 2 years to do the diploma, but I did that because I want to go into nursing, they also do a National Certificate which only takes 1 year.
I think an NVQ is your best bet, and lots of companies and agencies will employ people to work in residential homes or as support workers with no qualifications, then train them for NVQ's whilst their on the job.
After you've got your NVQ you could then apply to a hospital, although I know a hospital local to me was applying for HCA's recentley and it said experience wasn't required.
Alot of people I know work in residential homes or nursing homes and didn't have any qualifications when they applied.
Or if you're feeling like going wild, you could always train to be a nurse. It takes 3 years to do the diploma, you need 5 GCSE's and are paid a small bursary of �500 a month while you train.