Not to mention that if you have resided outside of the UK for a serious length of time, the NHS could possibly charge you for their services - as they have done with Brits who move to Spain and then return to the UK merely for medical purposes, because they feel as they've paid into the NHS, they should still get to use it even though they no longer live in the UK.
I'm not saying I take a side in it - I'm just stating that this is what's going on right now here. But if you're going to use a private centre anyway, this may not be a problem.
Personally, I would rather stick with the same OB/GP/midwife throughout my pregnancy through to birth - but that's just my personal feeling on it. My mother switched OB's 2 months before I was born because the one she started with wouldn't let my father be present at the birth (this was the late 1960s). So, at 8 months pregnant (I was a month late!) she found one who would. And she was fine with that.