Hi Bellbell, I can't give specifics about the hospitals you mention but I wanted to comment here anyway as my experience may be able to help you out.
I am in East London, and was choosing between Homerton and the Royal London. Ideally my heart was with a home birth but I just didn't have the strength for that in the end.
I went to see the consultant midwife at the Homerton and have a guided tour of the unit and the room I would be in. I got the hospital protocols and looked at what they would want me to do if they completely had their way. I did the same for the Royal London where I was booked in anyway, and after much deliberation I decided to stay there.
The starting point for both hospitals was very similar. (Epidural, CFM, slightly different time limits for 2nd baby, etc. Very interventionist). At a fairly early stage I went through the protocols with a consultant to get an idea of what they were flexible on, as at the RLH the protocols were written a good few years ago so were out of date. And then I researched the rest and decided on what I wanted and what I was flexible on in order to make my birth plan.
At the Royal London I did NOT have to be in the theatre, but at both hospitals I found the larger rooms required for twin births to be very institutional and, frankly, GRIM.
To cut a long story short I negotiated use of the pool at the RLH. They agreed to me having intermittent CFM, meaning that I would have a 20 minute trace done every 2hours, so I would have had to get out out of the pool every 2 hours (but I knew it wouldn't take that long). Then I think I agreed to get out of the pool for delivery of t1 when I got the urge to push.
I was VERY firm about only having the lead midwife and another midwife in there and for all updates and discussions about my progress to the consultant to be done outside of the room.
What else? Oh, yes, T2 was breech. Initially frank breech but after t1 was delivered her feet came down and I think she was flexed. At the RLH they are a lot happier about breeches for second twins and they will not section, but different consultants have a different level of jitteryness with regards to them. The first consultant with me was quite nervous, but thankfully she went and another took over who was very hands off. Before t2's birth he said to the midwife "in these situations we find the breech births itself" so he was remarkably hands off. And my little T2 did come out very easily all on her own.
I researched the time interval between twins and found that there were different guidelines all over the place. Which lead me to believe that noone really knew what was best. I got them to let me try for 30 minutes before starting with the syntocinon, but we actually left it 50 minutes, and then I waited another hour before having my waters broken. The gap was nearly 3 hours - but I wouldn't recommend that. The separation from t1 was not nice.
I don't want to go on and on about my own labour, as that is not what you have asked for, but what I am telling you this for is so that you know that you CAN get them to compromise, don't take the first no for an answer. And as different hospitals will do different things then surely that means the risks are not proven adequately?
I found the paucity of research and information for my particular situation very frustrating and the fact that so few people seemed to have done it naturally it made my battle feel like quite a lonely one.
As well as the information Mars has given, google a woman called Karen Gromada. Link here. She has a draft birth plan which is good for helping you think about the issues in the articles page. She also has some photos with breastfeeding positions for 2, but I found that a bit scary antenatally!
Congratulations, there are plenty of healthy normal twin pregnancies so try to enjoy yours and not let the worry mongers get in the way.