Another thought. NCT support doesn't stop at birth - I went to baby groups afterwards, too, which were a lifeline in the early days once DH went back to work.
I didn't do the whole coffee morning thing but could have done if I'd chosen to, for as long as I still had a child to take! I'm not an NCT member any more, but TBH if we had another one I'd probably rejoin to get back on the mum-and-baby circuit.
Yes, there is a class thing in there as NCT classes are fee-paying (though my branch would waive that for a couple who were out of work/ on their uppers, I never met anyone who that applied to - maybe no-one knew about it or didn't feel comfortable coming on that basis, I don't know). DH and I did note that we came to classes in the oldest/ scruffiest cars on the car park, by some distance!
BUT for me, it wasn't so much about class as about age, IYSWIM, as on the average MC mums tend to be older and therefore more like me (33 when DS was born).
I went to other baby groups run by the local HVs, and they were lovely and we stuck with them, but if I wasn't pretty careful I'd end up sat next to someone who was young enough to have been my daughter, and who saw me in that light. Again, that's fine and I met some really nice younger mums, but it's not all that great for proper peer support really IMHO.