Hi Ellie and cej,
I achieved a 2.1 from a low ranking uni (around the 70s/80s). I too got a couple of thirds and 2.2s. The bigger firms (magic circle, silver circle, US, large national/regional) will have a mass of applicants with grades that are probably consistently 2.1s and firsts, so this may pose a few problems in your applications to those.
However, smaller firms, who are less likely to have auto filters and who judge your application holistically, may see something in your application that mitigates those lower grades.
After three years of trying I recently got a TC offer from a small regional firm. I was grilled in my interview about my lower grades; one interviewer even called my Trusts mark 'poor'. However I was able to explain my reasons for getting lower grades and tried to swing things back into the positive by pointing out some of my better grades, which were in areas the firm specialise in. You can put a positive spin on these things and I know a lot of people with a few poor grades on their transcript who have been successful.
I am sure you know this and you have read the 2013 threads etc, but just to remind you how tough law is and that there are many excellent candidates who are still hunting. If you want any more advice, please PM me your background and hopefully my (many) years of experience can help you a bit.