Note: I have completed my bachelor's in Computer Science.
Student life, in partnership with UEA
If you just want to be a designer, the best bet is probably an online course like Shillington where they'll teach you loads of skills and develop your portfolio. Very few Masters courses actually teach you the core skills, because it's assumed you've already done this on a MA course.
Literally nobody in the design industry cares if you have an MA or not. It's all about you and your portfolio. The exception to this rule is if you choose to do a specialist MA which doesn't tend be taught at undergrad level (like service design or typeface design).
If the qualification is more important to you, then the MA courses at the best-regarded Unis are expensive. You're very unlikely to find a funding or a scholarship. It's just the way it is.
A couple of other options: the PG Cert and PG Dip Visual Communication courses at LCC are designed for people in your situation - moving from another field into design, but they're relatively selective who they let on (unlike a lot of MA courses who are desperate for numbers). Also, Falmouth run an online MA which is cheaper but still pretty good.