Not sure exactly where you live, but when my brother was living in Winchmore Hill (near Enfield), he and his wife opted to have their first two babies at the Royal Free Hospital (NHS) in Hampstead. A bit of a drive, but they felt it was worth it. When I was pregnant in the UK, I was told that technically you are entitled to give birth in any hospital in the UK. So worth investigating other hospitals in the area, even if it means a bit of a drive. You will want to know you are going somewhere you're happy with when the contractions set in!
I was living in Surrey and opted to go to an NHS Birthing Centre in Crowborough West Sussex. It was nearly an hour's drive away but the facilities and level of care were so much better than at my nearest hospital (Redhill). I stuck with my local care throughout the pregnancy until about the last 4-6 weeks, when I started having check-ups at the birthing centre. Turned out I had complications during labour and ended up being transfered to a hospital in Kent, so didn't work out the way I'd planned! A long story!
Unfortunately there aren't many NHS birthing centres in the country.
But as I said, it is definitely worth looking at all the options and don't feel pressurised into using your nearest hospital if you're not happy with the level of care etc.
Hope this helps