Granted I haven't had a baby through the NHS but my last experience in the Lindo wing was a very quiet and private room to give birth in (meaning the Lindo Wing's labor ward was very quiet and 'calm') had my own bathroom to have a shower in, the same midwife attending throughout my birth, etc.
Every woman admitted to any NHS hospital gets a private (as in just for her) room to give birth in. NHS Labour & Delivery wards are generally a corridor off which are lots of individual rooms in which women are labouring. How quiet it is depends on how loud the women in neighbouring rooms are!
Your delivery room in an NHS hospital can be quiet, calm and dark if that's how you request it (I recall having to be woken from a comfy slumber in my quiet, dark room to be told it was time to start pushing when I had DC2).
I've always had my own bathroom with bath/shower/toilet/sink in NHS delivery suits.
If you manage to labour and deliver all within one shift change, then you are likely to have the same midwife in NHS. Like you get a 'named nurse' on general wards, you get a 'named midwife' in delivery suite. But if you labour through a shift change then you get introduced to your new midwife, taking over the shift from the previous one.
Given that I have long labours and have several times spent over 24 hours in delivery suite - I would assume it impossible to have the same midwife throughout, private or NHS. Surely that would be highly unsafe due to the lack of sleep?
So all-in-all - I have had four children in NHS Nottingham City Hospital in and have not had all that different experience to private healthcare, it would seem. Good old National Health Service 