I've just had a baby in Canada (also a national health service) where I had a private room with throughout (although a shared bathroom with the next room for the couple of days I was in after I'd had the baby).
I was induced, so monitored continually for 3 days (on a mobile monitor) and when they switched to syntocin (after the whatsit up my hoojamaflip didn't work) I had a nurse in with me continuously
I was encouraged to be in whatever position I wanted (or wander the halls), and when it all got too much I was offered my choice of pain relief and had an epidural within 1/2 and hour (one of the ones on a drip, so it could never run out).
When nothing was working, and the baby was in distress there was a full discussion of my options, and again within 1/2 an hour of a decision I was in theatre (at 11 at night!).
After theatre I was in recovery for an hour (again, with continuously watchful nurse) then brought down to a new room where I was helped to feed my baby for the first time, a couple of days later helped to wash him, and generally was given care that I just couldn't fault from fantastic doctors and nurses.
That is what a national health service can be, BUT it should be noted that here I don't get free prescriptions, or free dental care, I don't get a health visitor checking in on me (past 6 weeks when the midwife stopped - and I had to go to her for the last 4 weeks of that)
In the UK you get an awful lot paid for that you just don't get anywhere else, and the money has to come from somewhere