Possible to get into top law firms with low grades but in russell group university?

Yesterday, on results day I BBC (Bs in Bio and Chem and C in History) with an A in the EPQ which I was disappointed in especially in History as I was expecting an A* to A with a B being the worst case. I was lucky enough to still get into my firm, the University of York due to completing the YESS and Yorjourney programs which lowered the grades from AAA to BBB.
I would like to get advice on what I could do next to aid my chances as I am aware that some top law firms require AAB to become a solicitor there. Once I am enrolled I plan on speaking to the careers advisor about what I should but I am aiming at getting a first class in all 3 years in law school and doing vacancy schemes during the summer holiday to start networking.
I would like to know if all this could still allow me to get into these type of law firms and is there else I need to do or should I consider a different career