I'm assuming you're in your first year at present and so are not yet at the stage of applying for vacation schemes?
The brutal reality is that the larger law firms receive approx 2500 applications for the 50 to 100 TCs available. The competition is intense.
When faced with that number of applications, the law firms have to undertake some form of filtering process. The first filters are degree level anticipated and University attended. If you're on course for a 2:2 then your chances are enormously limited. Unfortunately, your chances are also limited if you attend a less well known/regarded Uni such as Southbank.
This is not to say it is impossible to get a TC with a largish London law firm. However, I'd suggest you need to be aiming to get a first so your application isn't immediately dismissed. As the previous poster suggested, you should also be filling your time with as many extra-currics as possible including taking positions of responsibility if possible. You need to make yourself stand out of the crowd even more than the average applicant. It sounds unfair, but law firms aren't charities and unfortunately you've got to be pretty special if you don't come from one of their recognised Unis.
Now, this is all predicated on the basis that you're interested in applying to one of the larger law firms. Clearly your chances of a TC improve if you widen your net and look at smaller London firms or firms outside the capital. That's not to say there's no competition for those jobs, but you are likely to have more success.
I'd suggest you blitz the vac scheme process when that comes round again but start giving some serious consideration to the smaller firms rather than the MC firms discussed on this board.