Because you referred to firms, I’m assuming your ambition is to join a commercial law firm.
It is a bit of an odd question because MANY people from UCL go on to secure training contracts - you are already in a competitive position by being there. You will, within your first few months there, meet many future trainees in the academic years above you.
With that being said if you wish to pursue studying at Oxford, it’s definitely not going to hurt your prospects. But you are already well positioned to do well if you work hard and make the most of your opportunities at UCL.