At least A*AA for most of those universities, and you have to actually love your subject and be well read. The thing about Oxbridge, Durham and the UoL universities is that they interview you and see how much you love your subject and how much you know outside the given curriculum; you can't just be a bookworm and expect them to let you in.
Also, do A-levels in traditional subjects; Economics, Maths, Sciences, English Lit & Lang., Philosophy etc.
for a level to stand a good chance at getting an offer you will need to get 4 A's at AS and be predicted around 2A*2A or more for a level . people do get offers with just A*AA but the majority have a lot better.
Also take further maths as a 4th a level will help you a lot. I wish someone told me that before as im now have to self teach it myself, but that is one of the reasons why i think i have my offer.
I would say you almost certainly need further maths. And something like A*A*AAA for lse or Cambridge, though it would depend on your school etc. You also cannot study straight economics at Oxford so you'd need to consider that as well.