Deffo not left it too late - and don't worry about your LO....apparently they don't really start to 'play' with other babies until they're toddlers anyway!
I think for the first year, mum and baby groups are more a way of getting you out the house as others have said. Agree that doing a specific 'course' might help, as everyone will be 'new' in week 1.
Does your local authority have a Childrens Centre near you? I live in SE London and our local Centre is really good, and runs regular 5 week courses of baby massage, which cost about £3 per class. That would be a good way to meet other mums with little babies.
Or if you don;t have a childrens centre nearby, maybe just google 'baby massage ' and I am sure there will be a private class nearby, which may be more expensive, but probably has better biccies??
Also, I found that lots of churches locally run mother/baby groups in their church halls on different mornings in the week. In my experience these have been good places to meet a real mixture of different women, some with older children/toddlers who are all dead keen to have a cuddle with a scrummy little newborn, which means you get to have a hot cuppa whilst someone else cuddles your baby! Some of them are a bit 'churchy' (obvs!) with a bible story and a song at the end of the session for the older children, which is not really my thing, but I figure whilst DS is too young to understand I can cope with that!
Good luck, and be brave!! Maybe see if there's someone else sat on their own and go and say hello? or a smaller group of two or three mums having a chat? I always find this sort of thing mega-cringe but I find if you go over, plaster on a smile and say something like:" Hello, would you mind if I sat here to have my cuppa? It's my first time at the group, I don't know anyone" people are usually very accommodating, then start asking you about your baby, her name, how much did she weigh at birth, where did you have her etc etc etc and before you know it you've been chatting for half an hour :)