Yes the NCT, is at a local level, is very middle class and what is wrong with that?
Degree level educated middle class mum's can feel very isolated indeed.
Very many of them have since they were 18 lived in away from their families and many may have moved several times.
If, as I did you commute to work in the nearest large city, you have absolutely no local friends.
When I had DD1, I knew a few local mum's with older DCs because I ran the local Brownies, when I had DD2 we had moved and I knew absolutely no one.
In both cases the local NCT was an absolute life line.
The house I lived in when DD1 was born no way big and posh enough to host coffee group, (it was a scruffy ex-council house, small and as DD was a baby unchildproofed).
No one worried, I went to bumps and babies and coffee at other peoples places and did my bit by type setting the local magazine. Something that having just finished writing up my university research I was set up to do.
Both here and back there most of the NCT people I've met and certainly my second antenatal class are well educated, but very variably well off.
I still have the scruffiest house, and neither the largest or the smallest income and 11 years later many of my last antenatal group are still friends.