Hi Juls, I am due to have my baby here in the next few weeks too.
As far as I know, you cannot book/pay for a private room at all.
My midwife told me - You are more likely to get to remain in your private room and not moved to a ward of 4 after delivery if you have had a difficult or very medical birth. However these rooms were built as birth and recovery rooms, the intention was that you would be able to give birth then stay in the same room for the rest of your time there. So when they are not too busy they do let you do that.
Having said that, they do seem to busy a lot of the time from what I hear!
They are not too strict about dad visiting times, I have heard dads can hang around and just be there with you, though I'm not so sure about staying the night, night after night if you need to stay longer than 24 hours.
hope everything goes well for you! when are you due?
I'm going there tomorrow to the labour suite to have an attempt at turning my breech baby, so if I find out anything more I will let you know!!