The unis targeted by MC firms usually make their law fairs open to any student of any degree take contact with them in order to pursue a future legal career.
I'd say: Oxbridge, LSE, UCL, KCL, Durham, Warwick, Exeter, Edinburgh, Bristol or Nottingham.
These are the unis that all MC firms target in a way or another. So if you pick any of these, no matter what the nature of your degree is, you can apply for TCs or GDL and have reasonably good chances of succeeding.