Applying for anything at oxbridge requires top grade - you compete with people with top grades for a small amount of places. if you applied for a second degree in anything you get no funding - you must pay it all. If you pay for a degree with minimal funding (medicine, veterinary medicine or dentistry), you can apply as a graduate for an accelerated course, in which you compete against other graduates only rather than school leavers. I mention that because I'm applying for Veterinary Medicine as a graduate in October (if I get an A in the extra a-level in Chemistry I have taken this year) - roughly 13 people apply with A* and A grades, and only 2 on average get in each year. Even the top grades struggle. Even with my current A*A*A grades, a pending extra a-level and on track for a first in my first degree - I still don't think my chanceS are great. So You See, to have any chance you need the best and even that's no guarantee.
A 2:2 shows you struggled with university, and oxbridge will demand more of you. Oxbridge demand more, in a shorter semester time.