Giddy -I had the same problems as you three years ago. We moved into Kent from London to a large village. I had a newborn and an 18 month old.
I was alone all day, didn't drive and had no family or friends in the area.
I did join the mother and toddler group but it was only once a week and there was nothing else to do in the whole area. Not driving made it more isolating and I confess I hated it.
My way of trying to find support and a community atmosphere was to join the local church. I don't know if you're religious and although I am, I originally went in order to get my son christened as a way of breaking the ice so to speak. Everyone loves babies so I used my son as a focal point and took it from there.
Eventually, we moved back to London. I realise you are not in a position to move, but would definately recommend joining a local church for community support and a friendly face, if not the religious aspect.
Most churches do try to be inclusive of everyone and you might feel less out of place and accepted. You really don't have to have a strong faith to go to church! I go as much for the social side of things as I do for my beliefs. I'm sure people would welcome you, no matter how little faith you have.
They do coffee mornings, charity work and fund raising events which also gets you involved with something else apart from your baby until you return to work. I know it all sounds rather twee, but that support certainly helped me through.
You will probably find people of all ages and backgrounds at church who are more likely to be sympathetic to your situation. I found some older mothers in their fifties and sixties who've gave me a shoulder to cry on and advice when I needed it far more helpful than any mother and toddler group.
I have made some good friends at my church here in Bromley and there are always other children for my 3 to play with, at Sunday School, events etc.
I would keep going to your playgroup if only for your son's sake so that he has some interaction with other children.
As for some of the comments I've read on here about you being a snob- well, I don't agree. My understanding of a snob is someone who has money but looks down on those who do not.
Respecting others treating all you meet with same polite approach is a mark of good values and upbringing. Just because you do not have anything in common with these other women does NOT automatically make you a snob. It only becomes snobbery if you consider them beneath you which is not at all what your post suggests.
I don't have anything in in common with my neighbour who is a childminder, but she's a nice girl, I respect her and always say hello. Just because she doesn't read Jane Austen and I do, does that make me snob or do I think any less of her as a person? NO!
You simply have had a different upbringing with your own tastes and interests. Village life can be very insular and hard to adjust to, so take heart.
I would advise you to try and pursue your own interests while remaining on good terms with the girls at playgroup as you say they are nice. Just talk about babies, have a cup of tea and leave it at that.
Join a book club, check the local library/newspaper for adverts and events which interest you, surf the internet for local groups, etc. If there is an adult education college near you, what about a short course on a Saturday or weekday evening? Try History of Art, Cookery etc.
I think you should try and persevere, as adapting will take time. Going back to work will really help and focus you again on the future. Get out for walks as much as possible! Good luck