I had a baby at QEH in November. I definitely do not recommend it. As others have said, it's way too busy and under-resourced. Possibly other London hospitals are also busy, but one difference to consider is visiting hours policy. You should check, but I think both Darent and Princess Royal allow partners on the postnatal ward 24 hours a day, but QEH only allows them during visiting hours, so you're on your own to take care of yourself and your new baby overnight.
I didn't take this into consideration, thinking I likely wouldn't be in hospital for very long, as my pregnancy was low risk, but things ended up not going so well, and my baby and I were there for over a week.
If you do go with QEH, don't make any decisions based on any timescales that staff use, as everything takes much longer. For example, my waters part broke and I was in slow labour. Staff told me they would take me to the delivery suite and fully break my waters once it had been 24 hours, at 10pm. But 10pm came and went without them having any available rooms, and I had to wait until noon the next day
. If I'd had any idea it would be so long, I likely would have made very different decisions about pain relief.
Delays of that length happened again and again, not just to me, but also to other women on the ward. So, every time someone says something will happen in some amount of time, you need to assume you will need to wait many, many more hours and make your decisions accordingly.
I could rant about QEH for much longer, but I guess I won't. Overall, it was a horrible experience.