I would guess your potential supervisor would probably care more about your lab/research experience than about your undergraduate exam results, especially if it's very relevant to the project you're applying for.
However, I think a 2:2 can sometimes be a problem in terms of eligibility for funding; some studentships have strict criteria and I'm not sure how flexible the institution would be able or willing to be (although you have nothing to lose by asking).
If it's a problem, you could consider doing an MSc first (I'm assuming the 2:2 was for an undergraduate 'Masters' like an MSci/MChem?). Or is there any chance your current employer would sponsor you to do a PhD?