What do you mean by a London law firm? Do you mean a big MC-type law firm, or any old high street firm in London? You’ve still got a chance with the former, but it’s worth noting that most TCs are given to RG uni graduates. Equally, though, I’ve seen plenty of trainees from non-RG universities in those firms so I’d focus on getting a first + good extra curricular. As to the latter, you’ll be fine with Leicester too.
It’s also worth noting that firms do still have A-level requirements. ABB tends to be the lower end of that spectrum so as long as you’ve got AAB you’re set. There are also firms who don’t ask for A-levels so you’ve still got options there.