I had an elective CS fully covered by (expat) insurance at the Portland. I stayed the full five nights I was covered for, even though I was declared medically fit to be discharged on days 3 and 4...I just didn't want to leave!!
It was like a fabulous five star hotel: three course meals, wine list, afternoon tea, spacious room, 24hr nursery and fold out bed for DH - absolute bliss!!
My sister was exactly the same number of weeks pregnant as me at the time, and couldn't believe the amount of support and care I got as a patient post-birth - I had a revolving door of specialists popping in to check on breastfeeding, wound healing, physio etc.
By contrast, she had an EMCS at St Mary's ten days later, having been sent away from the birthing center there due to meconium in her waters, and had a terrible experience: overcrowded and hot six-bed bay with patients moaning out in pain; and too weak to get up and tend to her newborn (my DN) and of course my BIL wasn't allowed to stay overnight.
If your insurance covers it, I say go for it, it was one of the best experiences of my life!!
I had consultant-led care on Harley Street from about week 28 of pregnancy - they usually offer different packages depending on when you want to start seeing your gynae, and the price reflects how many scans, tests, appointments etc you need based on how far along you are.