I couldn't not post because you seem to have got yourself in a bit of a tiz It was the 'has anyone had a baby here?' question here on nappyvalleynet in the heart of nappy valley judged by some to have the highest birth rate in Europe (or is it per capita?) have you seen the number of pushchairs on the street?
Sorry I'm only teasing!
The NHS is quite easy if you have a problem you go to your GP who will then refer you on if needed, generally if you are referred you will be given a choice of hospitals (that is dictated by where you live-amongst other things) Part of the function of GPs though is not to refer so don't be disappointed if you do not get sent to see a specialist (much more normal not to)
TBH (IMHO) hospitals are all much of a muchness around here unless you have something vanishingly rare (which it's hopeful you don't) and things like parking, travel, visiting should be considered too.
Of course if you have something serious chest pain, broken leg etc etc then you go straight to A&E, ambulances are free. (dial 999)
Health care here is different from the states it is less consumer driven and of course funded by general taxation so not really set up for hand holding, sorry. Try not to get affected by the experience of others what is deeply upsetting to one is water off a ducks back to someone else! It doesn't mean that you will get substandard care.
So when you get pregnant go and see your GP (early) who will give you a choice of local hospitals, come back and ask us then what they are like because they do change with time they will then refer you on for 12 week scan and to see midwife, in the meantime you can think a bit more as to whether you wish to have private health care (some consultants will get booked up very early)
I'm not sure what you mean in the first para about programmes and benefits you normally get what you need due to cost constraints you don't get what you don't (my cousin the the States has ?monthly certainly regular paed visits etc which just make me laugh there is nothing like that here) there is however health visitors which some people find useful if you want to check stuff eg a friend was concerned about the way her daughter walked, they weigh babies too if you feel the need for that kind of thing, however I stress if you/your baby is ill it's the GP you need.
However if you've not been here long have you found enough to do? Do you know all about the places to go and the things to see and do from 1 o'clock clubs to music classes, battersea Zoo/National Army museum to NHS walks and nice coffee shops. Come back and ask if not.
There was a bunch of ladies from America trying to meet up on here a while ago I don't know if they managed it or not maybe try and message them too?
I hope that wasn't too patronising (telling you how to dial 999!!!sorry) try not to overthink it and worry too much about the things you can't control and enjoy Londonl