The crucial thing to do whilst studying an English degree in London is a) join the student drama society or comedy club and write scripts, also become a journalist on either student TV, radio, or print media, and try and get p/t work at an advertising agency, barristers' chambers, or for a London theatre. Dull people do dull things. Future employers want someone who stands out. Just doing studying for a degree is dull and means the person will have lower chances of employment. Those who have a portfolio of experience, with details about projects, articles that they have written, etc show gumption. Future aim for City to do Broadcast Journalism, BPP to convert to law and become a Barrister, and develop character and personality via drama/comedy - if you do this then go to The Edinburgh Fringe, as you will really standout, and will not be dull. This will give you a choice of careers, and drama sets up for education careers too!
Check out KCL and UCL student societies and student media. remember KCL is closer to the key theatres in London, so may offer networking opportunities. Look at the background of the Professors and Lecturers, are they interesting. do any of the halls of residence have drama clubs, as they would be key to target.
I don't know much about KCL or UCL, as I went to Durham and Edinburgh 9yes the Fringe was a deciding factor).
Forget about league tables, but do use LinkedIn to examine which universities journalists, literary agents, dramatists, etc go to at The Times, BBC, etc,
Drama experience - don't forget that English opens doors at NFTS too! Today...London, tomorrow Palm D'or and Oscars