DF, I'm due to give birth at the Heath in a few weeks ELCS - and it is very confusing working out what the arrangments/options are, IMO. And yes, it has had some awful press in the last few years.
They move you out of the delivery suite (single bed room) as soon as they are happy you can be looked after on a ward, which is normally a matter of a few hours after birth as far as I know.
I've been told there are private rooms but no guarantee you'll get one, and there aren't many anyway.
A mate had an emergency CS earlier this year, and had to spend a couple of nights on the consultancy led maternity ward (C1? I think that's what they call it), which she hated (crowded, busy, loud, no privacy etc - curtains round the beds, but the beds very close to each other....also said there was little privacy in the shower, and a lot of blood!). The MWs are very cagey about C1 when asked, which I found alarming...
But then there's the MW led unit at the Heath too, which I gather is the 'new' one, and that seems to have either individual rooms, or be shared with only one other mother. I could be wrong, but that's what the MW said when I asked a couple of weeks ago.
I wish there was some external 'resource' which told you these things. Even knowing if you'd been in a 3 bed ward or a 20 bed ward would be handy....