Where I live I could have gone to a donation based group every day of the week had I wanted to. Surestart centres were still around then. They were amazing, even offered free lunch to ANYONE, no need to say if you were on benefits or drove a Jag.
Every single toddler group I've ever been to (and I went to many over the years) was welcoming to everyone and free to those who had no money. Donations were welcomed, but it was always done discretely on an honours system and no one would have turned a single mum away - actually, no one would have known whether she had paid or not. All groups offered tea/coffee and biscuits and snacks for the kids (lots of fruit, veg, toast, that type of thing). There was often food left over at the end which people were encouraged to take home (stuff like carrots, bananas, pint of milk, etc.) The volunteers who ran these groups were pretty good at looking out for everyone and many parents were helped by pointing them to services (not just poverty related, but things like speech therapy, sleep clinics, breastfeeding clinics, etc.) The support I got as a new mum was incredible and I'll be forever grateful to the various volunteers who took the time to make me a cup of tea, listen to my woes (I haven't slept in months!!!! I'm soooo tired) and gave gentle and helpful suggestions.
While there is much wrong with society, there are also lots and lots of wonderful people out there, willing to listen, help and give practical advice. However, if you are too proud to ask your family for help I suspect you won't want someone from a Surestart centre or the local church to 'interfere'.