There's a Banana, but it's like, double the price of Banana in the US. I don't find it worth it. (And I was a dedicated BR fan for years.) But they do carry the petite line, and it's true to size as to how it is in the US, so there's that. I believe it's on Regent Street, right?
In terms of petite stores, I haven't found a lot of luck although many of the high street stores (Uniqlo, H&M, Topshop, Gap) have petite lines. I haven't found an Ann Taylor type store yet, though. (You pretty much named every store I'd shop at at home).
For most of my clothing purchases here, I've been sticking with the Gap, Uniqlo, the HaM, and sometimes Jigsaw, if on sale.