I gave birth to my first child at the Whittington 9 weeks ago and, personally speaking and based on my own experience, I couldn't fault them. I had a great birth experience, and I am sure that was as much down to the hospital facilities (had a waterbirth in their amazing birth centre) and the wonderful midwives/staff as much as to my body being kind and giving me an easy(ish!) time of it.
I don't know if you would be able to have your own room immediately on arrival, either on the labour ward or in the birth centre, if you were only in the early stages of labour when you showed up as I get the impression they are pretty busy and rooms are needed for those further along the line. You might be placed on a ward for a while until you've progressed a bit further, but if you live close to the hospital and go in early, they will probably suggest you go back home for a bit and come back later (which is what happened to me) and which I found preferable. By the time we went back later on, my labour was much more advanced and we were taken immediately to a room in the birth centre where we remained for the birth and afterwards. For the first bit I was just with dh and one lovely midwife. It felt very private, I think another midwife might have popped in to have a word once or twice but they always knocked first and I definitely felt my space and privacy were being respected. After the first midwife finished her shift I ended up with 2 other midwives and a support person (+ dh!) and although this was more people in the room than I had originally envisaged when I wrote my birth plan, I was really glad to have them all there. They all sat around the edge of the pool and I felt so totally safe and supported having them all there, it was amazing. As for hearing anyone else labouring in another room, if there was I wasn't aware (they might have been aware of me though, I was that noisy person!). For me I felt like I experienced the whole labour and birth in the birth centre in a sort of protected and intimate bubble, if that doesn't sound too strange.
As soon as dd was born and pronounced fine, and I'd been stitched up etc. I had a shower in the ensuite shower room and by the time I came out the bed had been tidied and made up and dh, dd and I spent our first night in the same room as a little family. The midwife who had been in charge of the birth came in a couple of times to check on dd but otherwise we were left to sleep/recover undisturbed. The next morning they brought me and dh breakfast in bed, and later on lunch as well! DD had been born at 10pm, about 3 1/2 hours after our arrival at the birth centre, and we were able to stay there in the same room until about 6pm the next day.
So, that was my experience of the Whiitington, and (as you can probably tell!) I was very happy with it. :)
HTH, if you want to ask anything else please feel free!