At the children's centre, the health visitors can let certain mums join groups for free if they think it's useful, otherwise it's usually £1.50-3 depending on the session, sometimes there's a free creche for something parent related. They also do family fun days and other events that are free every now and then.
Two local churches have a free group, another has a mix of free and paid for, another is £2.50 but has a sign that you should just fill in the tickbox on the form if you can't pay for the session. I expect that the other church sessions at £2-3 would also let someone in for free if they ask quietly, I just haven't noticed signs. A Lionel parents centre that I think might be a charity has specific free groups for young mums, mums of multiples etc, though they also have paid groups it's only £2.50. Soft play is £2-3 depending on age I think, I don't go yet because the noise is crazy.
The Hoop application includes some free events and anyone can sign up for free taster sessions; you can try out 10 things at least to give something different to do each week without having to sign up. Those tend to be £5-10 classes normally, so it's worth doing. SIL and I explored several areas with our two babies trying all manner of classes for free before we each signed up to regular stuff and lost interest in freebies for their own sake.
There are some breastfeeding groups and baby play areas, though a lot of stuff is in cafes or pubs so someone is really expected to get a coffee. An occasional one just getting tap water probably wouldn't be noticed nor minded. Then there are the playgrounds and a coffee stand near one where mums tend to gather and talk to anyone turning up.
I think the main difficulty is when someone is shy, because then they don't get chatting to other mums to find out what's free and cheap in the first place. Our health visitors seemed quite on the ball in asking if we go to any groups, if I'm meeting up with other mums etc, just a shame the council are currently trying to cut their budget. (Petitions signed!)