Robbie, the emergency services vary from hospital to hospital. I'm sure that UCH has the top level NICU facility, so most hospitals private or NHS won't match that. Eg, if you had a super premie (say 25-28 weeks) at Whittington, the baby still might have to be transferred to a higher level facility. (I'm not sure if they do the "level" system here. It's what they use in the US. My little sis had a baby at 25 weeks at a level II facilitiy, able to cope with a later premie but not a baby that early, and she was transferred to a level III facility many miles away via ambulance.*) If you're worried about that sort of thing, you should ask about the particular facilities at each hospital, NHS or otherwise.
That having been said, the Portland does have a NICU and emergency services available to its inpatients and admitting doctors. My friend had an emergency C-section there and it went smoothly and left her loving the hospital and doctors. I've given birth there and it was wonderful. My 4 1/2 yo son has been admitted there as an emergency case when he was sick with scarlet fever and the care was swift and effective.
Just wanted to point out that there are private hospitals that can handle most emergencies, in the same way that most NHS hospitals can handle most emergencies. The Portland does have a midwife-led service available also, if you don't want to have a consultant. The only thing I'd do is book with someone now as places fill up quickly.
*My sister's little girl is almost 4 now and ahead in most things for her age (not height and weight, but that's all!). In Illinois (in the US), all premies are given speech, occupational and physical therapy from the day they leave the hospital (or thereabouts) until they are 3. This is a state funded program and costs the parents nothing. There is a choice of doctors available, so if there is a personality conflict with one, it's easy to switch. It might not be obvious, but there are no waiting lists, no hassle finding someone and it's very open, so the course of therapy is dictated by the best interests of the child.