Just clearing up a couple of the myths that always appear on these threads
The Portland is the only private maternity option in London not based within an NHS hospital, and it does indeed have a neonatal baby unit, a baby intensive care ward and an Adult High dependency unit (one step down from intensive care)
In the event of you needing to go to intensive care, they transfer you to UCL which is about a mile away, but as of this time last year (when I asked them about it), that hadn't happened for 4 years. I always raise an eyebrow that 'lack of close proximity to ICU' isn't listed as a reason to avoid birth centres/home births/midwife units...
Petal also said if you go to a private ward, you have to 'go running to the NHS for an emergency c-Section' - also not true. The lindo, Kensington Wing, Westminster suite and Portland all do elective and emergency c-sections.
In some hospitals, the private patients get their own operating theatre, in some they share the NHS theatres, but if you start off privately, they don't turn you over to the NHS mid-labour to have a section!
Of course that means that even if you are planning a natural delivery, you should set aside some money to cover the possibility of needing an EMCS, as they will charge extra for that...
If you want to start off in the NHS system for scans and blood tests, with a view to transferring privately for delivery, it is entirely possible, but be aware that a lot of the consultants get booked up far in advance for their private patients. You should be ok if you contact them at 20 weeks, but you probably won't get your first choice if you contact Mr Duncan or Mr Wales at 32 weeks.
And if you are going to do this, keep it quiet from the NHS, as they will grumble at you about it (but I don't think they can refuse to see you, even if they know you are about to jump ship)