Hi, I'm in the same boat as you and had a difficult time deciding because the info online tends to be pretty dire. Also since I'm originally from the US, the whole system is so different from back home. However, since I've been here for over 10 years now, and having worked in a couple of hospitals, I am more familiar with what to expect on the NHS. Overall, most hospitals in London you will receive very good care and staff will be friendly. In my experience working at some of the big NHS hospitals, I don't think there are big differences in terms of the care that you get. You generally get a decent level of care.
When I was pregnant last year I booked with UCH, and heard back from them very quickly with information about my first midwife appt and scan, but I had a miscarriage before I got to my 12 week appt. I did go to UCH emergency gynae and the early pregnancy unit to be looked after during my miscarriage and the care was very good. Also UCH is one of the newer hospitals so the facilities there are a bit more modern.
When I got pregnant again this year, I was going to book with UCH again, but St Mary's is actually a little bit easier for me to get to so I decided to book there, as I did see some good things online and heard that their birth centre is nice. St Mary's was not as prompt at getting me an appointment, I had to chase them to make sure I was booked in. My booking appointment was pretty haphazard, they were understaffed that day and it seemed everyone felt under pressure. The building that the appointments are in is pretty basic, it is kind of like a permanent portacabin. I recently went back for my 12 week scan and the atmosphere was a lot more relaxed, so I think the first appointment was just a busy day. The sonographer was really friendly as was the lady taking blood. The receptionists both times are informed and can explain what you need to do and where to go.
I have been to the Royal Free a few times just for general blood tests, but couldn't comment on the maternity care there. The threads on here about Royal Free are pretty scary, but they are also pretty old.
I think the care at any of the hospitals will be good, especially if they are part of a teaching university. UCH and the Royal Free are part of the Academic Health Science Centre Network with UCL and St Mary's is part of Imperial College's AHSC.
If you are wanting a more modern hospital, UCH is probably the newest and shiniest, while the Royal Free is 1960ish and st mary's has some victorian buildings that are pretty old. However, st mary's also has the option of the Lindo wing if you are able to pay for private maternity care and I read that the Lindo was just refurbished and re-opened last year. UCH has also just introduced something called the Fitzrovia Suite or something if you want to pay for an elective c-section privately.
good luck with your decision. I hope some other people post on their recent experiences with these hospitals too as I'd be interested to see them!