with 'normal' grades

Hi brightest star. I reckon you should apply, regardless of what the websites say. My situation was somewhat similar to yours I graduated from a Brazilian law school in 2007 and my marks were rather normal (7.37 out of 10). However, I decided to apply anyhow. I still havent received any reply from Oxbridge, but Ive been accepted to UCL, KCL, QM and Aberdeen (got kicked in the ass by Nottingham, Edinburgh and LSE). So, out of the four universities you mention, if you happen to have the same fate as me, youll probably get offers from three! Doesnt look bad, does it? And dont go discarding Oxbridge just cause you think you cant get in It sucks being rejected, but youll never be rejected (nor will you be accepted) unless you have applied.

Try it.

Yes, try it !

It's always worth a try!

There are not only your marks that are taken into account! The univerities look for diversity and different individuals. So, your extracuricular activities, your cv, your personality are also considered. Therefore, you cannot lose as long as you do not try, but you also won't win!