I sympathise. Whilst posts suggesting all the obvious things - volunteering, a sport, a hobby - are well-meant and could work out well, it's not that simple, is it? Often clubs etc are very cliquey and people have their own friends and families.
It's a bit like dating: you need to know other people are also actively looking for friends.
I've recently started trying to actively make new friends. There is the Meet Up Facebook thing - I'm probably not using it properly because I just get loads of emails for things that aren't suitable. When I find a moment, I will investigate further. They do have speed-friending evenings though, although as yet I haven't been free to attend one. But, I realise it depends where you live.
I also stumbled across www.togetherfriends.co.uk
which I paid to join. Only one suitable match, really, in my area and she found me at the same time I spotted her. But worth the money (actually only £20!) as we've met up quite a few times and get on like a house on fire!
I'll try some of the other suggestions mentioned here. I do think internet friending is a great idea. And like, internet dating, it'll eventually be widespread with no stigma.
It is really hard to make friends when you're older. People move away, their interests change, you might not have anything in common anymore, they have families and jobs that take up their time etc etc. I did have some friends during the baby years but - to be honest - it was mostly dull and just passed the time. School gate was horrific. Never really found anyone I connected to like my university friends. My other ambition / task is to try and reconnect in real life with uni friends, but it'll take a bit of effort as we're all spread out around the place.
Good luck!