Polly, I had an emergency c-section first time round (at a different hospital) with a similar experience to yours - full labour, 10 cm dilated but baby in a funny position and couldn't be reached so ended up with c-section.
On the "unexpected VBAC", don't worry, they didn't force me into anything :). I described the VBAC as unexpected since in my heart of hearts I really assumed I would end up with another c-section. This was partly because I was overdue last time and was induced but the induction didn't really work so I somehow assumed my body really didn't know how to go into labour. Since UCH said they prefer not to induce after a previous c-section, I assumed I would go overdue, baby wouldn't appear/I wouldn't go into labour and so would have to be elective c-section. Potential pre-eclampsia towards the end of this pregnancy also made this seem a likely ending. Finally, the previous c-section was a good experience and I was getting cold feet about natural delivery so I was basically hoping for, and all geared up for, a controlled c-section. However, waters breaking at 38+4 weeks and then a baby 17 hours later (10 hours after contractions started), meant a swift rescheduling of plans!
So, my body really made the decision to go the VBAC route. If I hadn't gone into labour early, UCH were quite happy for me to choose whether to hang on for a VBAC or have an elective c-section.
Given your history, I doubt you'll be allowed to go to the Bloomsbury Birth Centre but, to be honest, when they're busy you go whereever they can find space. I think busyness rather than policy will determine level of monitoring and whether you can use the pool. Talk to them about the level of monitoring they would normally do. I didn't find it as intrusive as I expected and I think I was monitored slightly more closely because of the high blood pressure towards the end of the pregnancy.
Sorry this is a bit rambling. Just trying to snatch a minute to type. Let me know if you have any other questions :).