Universities and GCSE Results

I'd like to study Law at University, however, my GCSEs aren't particularly strong for top universities. I achieved three grade 8s, five grade 7s and a grade 6. Which Russell Group Universities do I still stand a fighting chance at?

Furthermore, would taking a law-related gap year after finishing A-Levels improve my chances at Oxbridge as I'll have received my A-Level grades?

Those grades are quite strong, you still have a fighting chance of getting into most of them. I would take a look at this thread for more information: https://www.thestudentroom.co.uk/showthread.php?t=6033950

I wouldn't just look at Russell Group universities as there are good universities that are not in the Russell Group (such as Bath). I wouldn't make a decision on a gap year just yet, as those grades are good enough for most if not all universities.