Most NHS hospitals allow you to pay for certain extra services. TV and internet access is common. In many hospitals it also includes being able to pay for private rooms with en suite facilities.
EDIT: Specifically regarding maternity wards: We did pay extra for a private room when my son was born, so I have first hand experience with that.
We payed for a private room as well. I did note that this wasn't something that was "advertised" but if you asked they were more than happy to give you a room.
Mind you this was 13 years ago in the old maternity hospital here in Edinburgh - don't know what the arrangement is in the new Royal Infirmary.
NB My wife gave birth in a private room in the midwife run "Normal Delivery Unit" which was fantastic - we only asked for a private room a few hours after she had given birth after she had been moved to a ward.
Generally the criteria is that clinical needs go first, so if someone needs a room, they'll chuck you right out again (and not charge you), which is fair enough, but also a reason for them not to create a too high expectation or demand.
Overall the NHS trusts have quite a bit of latitude in carrying out private services to offset costs by increasing utilisation of facilities and equipment (private surgeries are often carried out in NHS operating rooms, for example), but the extent to which they take advantage of it varies quite a bit.
Do you mean the private room? That wasn't a luxury option, I should have been more clear on that :-). All rooms are private, and though we got lucky and got one that was slightly larger than the others it didn't cost extra. I think the small fee they impose is simply meant to encourage people not to overstay.
I'm experiencing extreme envy at these private room stories.
I had my first child in a great hospital with the same room all to my family for our full two-day stay.
For my current pregnancy, I switched care providers, but I chose the new midwife based on her ability to deliver at the great hospital where I had my first child.
Last month (when I was seven months pregnant), my insurance company decided they no longer cover the awesome hospital. My midwife said insurance companies almost never let you stick with the hospital you'd planned in these situations. So unless I want to pay for the whole thing (despite being insured at great cost to my employer and me), I can spend my first days with my new baby sharing a room with some random family of strangers and their new baby, at a hospital where there's a high likelihood that the other family's new baby will be enduring significant medical problems.
Hooray for privatized health care, right? Clearly better than any other possibility.
EDIT: Specifically regarding maternity wards: We did pay extra for a private room when my son was born, so I have first hand experience with that.