Most of my mummy friends are from NCT (we all did our antenatal class together and now are kids are within about 2 months of each other in age). Obviously, if you didn't do an antenatal class when pregnant, it's a bit late to go back and do one now. But NCT activities in general are good because most people are friendly and it's the way that many mums meet new friends, so totally acceptable to just start up a conversation with someone. Otherwise, going to specific groups where you think you'll find like-minded people interested in the same things as you (forest school if you like the outdoors, natural parenting groups if you follow a natural approach to parenting, buggyfit type classes if you like to exercise). I personally didn't find I met other mums I stayed in touch with at general groups, like at the children's centre or the library, because I didn't have anything in common with them really. But if you go to something specific where you are likely to meet others who have the same interest, you're more likely to actually have something in common with them that you can build a friendship on. I met several people at our local sling meet and at a natural parenting group because we shared those interests, so ended up having a lot in common. Also, classes that people come to every week are better than just one-off activities or groups where people come and go week to week. It takes me a while to warm up to people, so chatting every week at the same class made it easier to get to know each other.
That said though, I think it's really hard to find mummy friends. It's nice to talk to people you see regularly at things, but I didn't always find I had much in common with them (other than having kids, but I kinda didn't want to just sit and talk about our children!). Frankly, I'm more just waiting until our usual friends who we've known for years start having babies (we're the first). It's a lot of work to keep those mummy friends relationships going once you all go back to work or get busy with other things or have another baby. None of us have the same schedules anymore, so can't manage to see each other. I'm hoping when friends and family start having babies, then we can still find time to see each other like we do now, but it will be easier because we aren't the only ones who have to go home early because of a 2 year old with an 8pm bedtime.