Hi cityangel,
I live in East London too- agree with toomanyshoes that you have to consider where you will go for your prenatal appts if you pick a hospital outside of the gps catchement area. I think this is v. important because if you have a low risk pg, you will have 9 months of appts somewhere, and only a few days in the hospital! (Although those few days are v.v. important, I know)
I think you can actually ask to go anywhere you want, but there is no guarantee they'll take you.
I have a lot of friends in East London who have gone to both Homerton and Royal London and the Homertons are mostly all happy with their experiences, and the RLs were all pleasantly surprised with theirs. A few minor bad stories thrown in, but I think those could happen anywhere. From what I've heard postnatal care in Central London isn't fantastic anywhere. And as for bugs, that can be anywhere too. I used to work at GOSH and they were forever closing wards for cleaning due to infections...
(btw, I'm booked in at the Royal, which means I have all my appts at my gp surgery (see the same midwife, easy to get prescriptions, near home, they know me, etc...) and I've got my name down for the Barkantine in March, all being well!)
ps. You can also change your mind at any time too I believe.
pps. My top tip for blood work- go to Barts on Tues/Wed morning on your way to work. Nice phlebotomists, no queues, and results v. quickly.