The target unis are pretty widely considered to include Oxford, Cambridge, UCL, Imperial, LSE, and Warwick (perhaps only specific departments there e.g. maths, the business school, economics, CS). Others may or may not be included by some peoples' reckoning but those are fairly safe bets I would expect.
I'd also note that plenty of UCL (and LSE) courses have the same or sometimes higher entry criteria than Oxford or Cambridge do in general. The standard offer for Oxford "arts" subjects is AAA typically - plenty of UCL courses are above that. If you are below that then with AAB or lower there are far fewer courses at UCL (or LSE) that you would be able to consider.
Also even if the entry criteria are lower in terms of grades, that doesn't mean the course will be any easier to get into. There are a number of courses at LSE with a given entry requirement of e.g. AAA or A*AA which have very low success rates for applicants (even lower than equivalent subjects at Oxford or Cambridge - for example law at LSE is usually statistically more competitive than either Oxford or Cambridge).
Worth bearing in mind quite a few investment banking grad schemes require AAB (and you will just get sifted out if you don't have that for those ones).