Will changing university help my chances?

If I change university will it help me get a training contract? What can I do?

I am coming to the end of my second year studying law at university, but looking at city law firms I have realised that the univeristy I am at will not get me into the kind of law firms I am interested in. So I would like to change university. How do I go about it? Will my two years count towards another law degree? Would I be better doing a non-law degree at a better university?