I just posted about this in the pregnancy area (didn't see this thread at the time). I have had two children under the NHS system; my first post-natal experience was on the public ward and it really was tough. I would not want to do it again, and was planning on getting out of the hospital as quickly as I could if I ended up on the open ward with my second child, who was born last week. Luckily, we were able to get a private room, and, man, what a difference! Soooo relaxing and calm and round the clock attention if you need it and just no pressure at all. If you can get a private room at your hospital, you will not regret doing so. Start saving now if it is a bit dear. We were charged £90/night which when you think about it is the cost of a mid-price hotel. It was worth every penny (pence?), and we had put aside some money for it ahead of time.
The room itself did not have its own bathroom but the ward had more than enough bathrooms for everyone -- I think it worked out to two toilet rooms and one bath for every three rooms? At any rate with all rooms filled there was never a problem with access and everything was quite clean and private. You only had to walk across the hallway to get to the toilet or bath.
When we were admitted my husband started asking about the private room, and when we were delivered he again asked and that is how we were able to get the room. I am not sure how busy it was.