Which universities should I apply for with these results

Hi, I'm currently stuck as to which range of universities, interms of ranking, I should be applying to. This is because I really want to go to a highly thought of university and want to study either a straight LLB or a joint honours qualifying law degree with a social science/humanities. But I feel as though my poor GCSEs will hold me back; even though I have achieved fairly highly at AS this year, after realising the importance of getting good grades and actually revising.

My GCSEs were BBCCCCCDDE
I also have just completed AS for the second time after having changed schools because of moving away and wanting to change subjects/improve my grades
My original AS grades were DU and a uncashed in BTEC engineering grade
However this year after deciding to restart sixth form at a new school I got;
A - business studies
A - Sociology
B - Law
C - Psychology
with the B and C possibly going up a grade each due to being 1-2 marks from the grade boundary and In the process of being remarked.
I am also hoping that by the end of A2 I will be able to achieve either AAA, after dropping business studies, or A*A*A

As for extra curriculum, I have visited my local courts a few times over the past year and also plan on applying to become a magistrate in my local area.
I have been involved in two student exchange programmes through my school this year to, Juangsu - China and also to kragerø - Norway and Completed a 'World Challenge' expedition to South India earlier this summer, although I'm not sure how relevant any of these are and whether to actually include them.

Any advice would be appreciated, I'm really liking the look of QMUL, University of Nottingham and Exeter Uni, although not sure how realistic any of these are..

If you are predicted the typical entry requirements (A*AA or AAA) then you have a decent chance. While some might regard your poor GCSE's as a handicap, others might see evidence of improvement.