I had my first baby at the Royal London. I was booked into the Barkantine and, in fact, managed to stay there throughout labour but had to be transferred to the Royal when baby got stuck. The Barkantine was great - this was when it had just opened in 2008 - and, medically, so was the Royal.
However the midwife I was allocated when I first arrived at the Royal was, at best, disinterested and, at worst, rude. The post-natal "care" was abysmal: filthy ward, no food or water offered after birth, no BF-ing care (I was discharged even though it said in my notes that baby "was not interested" in feeding aka hadn't fed).
Thankfully the Barkantine helped us sort out BFing and we had all our post-natal care there. Had I still been in London I'd have tried to have my subsequent DC there too.
The Royal has recently been rebuilt (as you must know) so should be in a better physical state. Don't know about the midwives though. Suspect it depends how heavily they rely on agency staff. Do go and look around it. As a PP said, there's a reasonable chance, as a first-timer, that you'll be transferred there.
Oh, and I think currently you can't book into the Barkantine until you're 36 weeks (and low risk). I don't know if this means you need to have booked into the Royal rather than, say, Homerton, beforehand.
Sorry for essay. Cripes...must get off MN!