Your undergraduate organisation is most likely to consider you for a Masters with a 2:2.
I applied elsewhere and was given an offer based on a First or 2:1. However, I was told by my programme leader that they would consider me on a 2:2 if I could produce undergrad coursework of a decent quality, which would be relevant to the Masters course for which I'd applied. Basically, my application and interview were good, they wanted me, so they were prepared to be flexible.
Sell yourself in advance of any application - email/meet the course leader and ask some intelligent questions about the course. Show an active interest. Make yourself the sort of candidate that they want, regardless of your degree result.