The timing thing is definitely as issue, yes. I don't often want to do things away from kids and DH on a weekend as that's the only opportunity of quality time I get with them. I would like to meet after work for a drink locally though, but haven't found anyone to do that with.
I also think my experience is coloured by having twins. Your are put in pre-natal groups with other twin parents (understandably, to get the relevant education), but meeting up with even small groups of twin mums in almost impossible – there are very few places you can go with three women and six babies. Baby groups are very difficult too as it's very one-on-one and difficult to manage two babies by yourself with many of the activities. So any socialisation is very difficult right of the bat – which may do some damage in informing the rest of your parenting journey even though twins aren't babies forever.
During the toddler years, I definitely found less mum's asking for play dates as they generally find hanging out with young twins more chaotic (which it is!), and then when they get to school age, they probably just want to invite one twin (the twin their kid is friends with) and not the other, but then feel awkward about it so don't ask at all!
I also think as a full-time working twin mum you just come across as being insanely busy all the time, and people tend to steer clear!!
Anyway, that's my sad monologue, lol. I hope you meet some nice mums in reception!