Someone in my family did an undergraduate degree in psychology, then a masters, then because the NHS paid for nursing degrees she did an undergraduate nursing degree.
She didn't pay for anything herself and graduated last year with her third degree.
Because you would've gotten on the nursing degree before the changes this year (in which the degree becomes the same as other degrees with student loans in the same way), I think you should be entitled to 4 years of funding (this is what Student Finance gives everyone).
I'm not sure they understand that your degree is different to other degrees because of the NHS (it's only changing this year in September 2016 for new students).
The people at Student Finance can be...annoying though. So they probably won't listen and won't give it to you, you may need to pay for the first year but you need to make sure before you drop out that you'll get a student loan for the other years and that you'll actually get on a course somewhere. There's no point in dropping out
Also, you DON'T necessarily need an undergraduate engineering degree to do a masters degree, a lot of engineering masters degrees that aren't integrated are actually MSc (not MEng) as they're considered professional degrees for people already in industry. If you contact a university though they'll probably let you on if you explain that you want a career change, it's just getting some work experience that you'll probably find difficult for your thesis, then getting work afterwards.
What sort of engineering did you want to do? Electrical/Electronic, Mechanical, Civil?