If you liked Birmingham (I did when I went there aswell) and the Social Policy course, have a look at Leeds. Similar uni except a bit less of a campus. Similar requirements so you can hedge your bets.
And although it isn't my field, I sat in to a friends open day meeting about social policy and it looked very interesting. Neither should reject you because of GCSE results because it is evident you have progressed throughout A levels and many people develop academically at different times to others.
Good luck anyway (I would say however that LSE seems to be a bit GCSE obsessed so possibly wouldnt apply there).