Don't watch the recent Panorama episode about private hospitals.
Or read books like "This is going to hurt" (I think it was).
Private hospitals can spend the money on looking nice and having larger visible staff (often a lot of whom may not be medical), they have zero requirement to be equipped for a serious emergency, often few or no senior staff on site outside of business hours, and may have little or no bloods on site.
Basically they're fine as long as everything goes as planned, but the moment something goes wrong you'd almost certainly have been better off at an NHS facility where they are required to be fully prepared for emergencies as most private hospitals will be calling an ambulance to send you to the NHS once they realise something has gone badly wrong (it's not "economically viable" to have things like a full emergency staff, pharmacy, bloods, testing etc on site if you're only doing planned ops and births).
IIRC the private hospitals also often won't do the "difficult" ops, or the "experimental" ones, so they'll do your bog standard hip replacement, but they may not do the second one let alone a specialist one (in the NHS the really difficult ones are done at specialist units*, but almost any hospital can do the standard ones).
*For example my local hospital routinely does standard hip ops, but if it's non standard it's likely done at another hospital in the area where the consultant surgeon has a specialist unit that has a lot more equipment/parts**/staff/OR dedicated to it.
**To avoid the sort of situation where they start an op and realise that the part they were going to fit isn't actually the right size/suitable and don't have a full set of options on site (apparently something similar happened to my mother in the 90's, she was opened up on the table and they realised due to the previous op the planned replacement and plan b were not going to work, so had to get an emergency courier in from another unit that held the "regional" stores).