I did NCT some years back, and others I know tried the NHS classes too (the NHS ones were free, so you can go to both if you have the time).
It sounds like the NHS course covers all the stuff about preparing for birth, but isn’t as good socially. The NCT class exchanged contact details for the members, arranged some meetups during and after the course and to this day we are still in contact with most of the NCT class (a few moved out of the area, but everyone else is still here).
So it depends on what you are after really, but I would not underestimate the benefit of making social contacts if it is your first baby - having friends to compare experiences with is very handy, as well as people to meet and get out of the house with while on maternity leave. I know some mums can struggle to make friends whilst on maternity leave, while others have no problems (there are loads of classes and groups around Forest Hill to meet people) - it depends on the type of person your are, but you’ll have more time and independence before the baby arrives!
So on that note, if your are thinking of doing a class with a view to making friends, I would say find a class closer to where you live. I know of a mum that went to a class in East Dulwich and then found it just a bit far to make meetups once the baby was born, so that didn’t work out as well as it could have.
Oh, and if it is your first, don’t worry too much about making a birth plan! Knowing the pros and cons for pain relief (meditation/breathing exercises, gas + air, pethidine, epidural etc …) and what you want are good (home, water, midwife led, hospital birth), but depending on how the baby comes the reality can be quickly different! Having a good birthing partner is a really good thing too.