Lindo Wing is lovely -- staff are attentive, food is fine, you get all the attention you need. You can do whatever you want birth-wise, and there is a nursery for the baby if you want to sleep. They bring the baby when it wakes to feed, or a minimum of every 3 hours.
Your consultant will probably order some tests that aren't done routinely on the NHS. Also, you probably get a lot more choice about antenatal appointments with a private consultant. I got more scans -- my consultant had a little ultrasound machine in his rooms and I could see the baby every time.
It was important to me to be in an NHS hospital (as opposed to say the Portland) in case things go wrong. Also, the money they make goes to the trust. (I think the Portland may belong to private equity investors, so profits go to shareholders. I am not sure about this, though.)
I have to say, we have private insurance that covers just about everything, and I am not sure it would be worth the money for me if I had to pay myself. I think this is going to run easily £14,000, plus all the little private lab fees and scans throughout the pregnancy. The things I have described are more or less luxuries. I am doing things the same in this pregnancy because it worked last time and it's what I know -- same doctor, same hospital, probably even repeat ELCS although it might not be strictly necessary. (I have to say I am glad I can just choose between VBAC and ELCS without having to justify myself, but not sure it's worth £14,000.)
In my experience, you do things privately for convenience and comfort. I don't think I would have got worse care on the NHS.