I think “mum and baby groups” is an imprecise label that encompasses both the types of groups that should be single sex and exclusively for mothers (such as breast feeding support or post natal groups where mums can talk about their experiences of labour/birth injuries etc) and social groups for young children and their caregivers.
The first type of group likely meets the threshold for single sex exemption in the EA.
IMO there is no need for the second group to be single sex. My kids are young adults now so I am out of date but men were rare in the social type group and I think the women were a bit uncomfortable by their presence (possibly evolutionary response when caring for an infant). However, more shared childcare and father involvement is a good thing and dads need social interaction too (as do the infants they are caring for).
The kind of group I mean is where you converse with other parents half a sentence at a time before having to prise your toddler away from snatching a toy from another child and manage half a (cold) cuppa and a custard cream if you’re v lucky.
Anecdotally, a young woman I work with told me that her husband was part of a group of dads who are caring for their babies - so perhaps it’s still difficult for dads to participate in parent and child groups in spite of there being so many more of them.
sorry - I didn’t realise I had so much to say on the topic!