I agree with y Ak17 - I've had 3 pregnancies, the first was a natural birth through the NHS at St Marys in Paddington where I only ever saw random mid-wives during my pregnancy - which is actually not ideal as you never have a continuum of care. We initially wanted to deliver in the natural birth centre but when my waters broke it was determined I was in high-risk labour so we had to be moved to the labour ward where they could monitor both our heart rates (which necessitates medical equipment you wouldn't otherwise get). What followed was 14 hours of excruciating pain, mainly due to the anaesthetist taking hours to administer an epidural. It was chaotic to say the least, but this is also in large part due to St Marys being a very old hospital compared to C&W. Our son was born naturally but I was left with physical damage.
This led to us deciding to get private health insurance so I'd have the option of private births with far greater control over the birth options, which is what we ended up having for our 2nd and 3rd kids at the Portland Hospital. I had the same consultant during the entirety of both pregnancies, the only time you see the midwives is the week before when they take bloods, swap you for MRSA, etc.
I did visit the Kensington Wing at C&W during my 3rd pregnancy as by then we were living in Battersea, so much closer, but I was really disappointed with it compared to the Portland Hospital, despite them being priced roughly the same. For example the Kensington Wing doesn't have a nursery where the midwives will take care of bubba so you can nap, the catering is pretty poor - most importantly, when I did the tour I found the staff in the ward to be very indifferent and distracted, some even playing on their smartphones, not chatting with the patients, etc. Totally different atmosphere.
If you have the option of either I would highly recommend the Portland Hospital, and if you're keen on midwife-led care I do think this is an option and you may well be able to have the same midwife. The only thing I would say is depending on how the pregnancy goes, if there are any complications that arise you'll inevitably need to be seen by a consultant - and if you've been seeing one throughout your pregnancy, it makes it much more reassuring that you already know them. I say this as my 3rd pregnancy did have complications from week 20 (placenta previa) and having already a close connection with my consultant meant I felt much less anxious.
Hope this helps.