I got a mid-low 2:1 (including on dissertation) but got a fully funded PhD. From all accounts, they were impressed with my written application and I nailed the interview. So you can definitely do it with a 2:1.
I think they will read applications from anyone with a 2:1 or above but you need to make yourself stand out to compensate for the low grades or have a very good excuse. Grades are good indication of how much you know/ work ethic so you need to be better than the other applicants in other areas. If you think you can do that go for it or even go for a self-funded one.
Though I was that guy that drank 4-5 nights a week and never turned up, so maybe I am just lucky.