I had a little boy last June (2019) at Queen Elizabeth Hospital. I live in Greenwich so it was a no brainer for me as it's so close. Like you, I had the choice of QE or lewisham hospital and I had a really similar approach and thought they both seemed pretty equal in their approach!
I have friends who delivered at the same time as me in both St Thomas', Lewisham and QE and all experiences were roughly the same. One friend had a terrible experience at st Thomas', which is surprising really because I expected that they would have the best care. Typically they do, but she was just unlucky.
I gave birth in the birthing centre at QE and it was great! My midwife was so lovely and I can honestly say it was a really positive experience. They were so diligent in their care towards me in the run up to labour. I really liked how close the birthing centre was to the labour ward should an emergency happen.
In my case I had a complication free labour, but I did have a medical emergency post labour with a severe post partum haemorrhage and had to go to theatre and then stay for a couple more days. Not saying this to scare you, I'm sure that won't be your experience - but more to reassure you about their care. The emergency took place in the birthing suit after my son was born and honestly the way they dealt with it was incredible. The buzzer was pushed, in a matter of seconds doctors, midwives and the consultant were in the room (so reassuring given it was a birthing suite- the point is that because the labour ward is down the corridor, if they need to intervene, they can quickly- so you're in very safe hands).
I did have a couple of more scares over the next 24 hours but the care was incredible and I felt perfectly safe in their hands. I was regularly monitored- each time a buzzer was pushed they intervened quickly and the day time midwives were so supportive and lovely. The anaesthetist in theatre was amazingly reassuring and so lovely and funny, the doctors were incredible - the midwives were amazing.
I'm sure that won't be your experience but if you do need some form of intervention, even if it's just wanting to have an epidural- you can easily get moved from the birthing suite to the labour ward- it's not far at all.
As a heads up they have private rooms available post birth that you can pay for if you would like your partner to be able to be with you that night in privacy. They aren't always available, but if you do go with QE, let them know you'd love to do this if it's something you'd like to go for once the little one is born.
I honestly think QE and lewisham are very similar from all I've heard- I'm sure you'll be in great hands whatever hospital you choose.
:-) hope this helps!