Would you feel confident sending round a group email to other mums in their classes before the end of term, suggesting a picnic in the park or a swim or cinema visit? Even if just one mum replies to one of the suggestions, you have something set up.
If your DC have any friends they'd like to see, instead of setting up playdates, call the mums and invite them over for lunch too. That way you might get to know them better.
Do you have family you could visit? Or who could come and stay with you?
Are there any churches in your area that run summer playschemes? Some of those are designed to encourage mums to stay and get to know each other.
If you don't feel comfortable being the one who makes the first move, then it helps to make plans anyway, just for the three of you, so you're not waking up thinking how will we fill all these days.
Book them onto a playscheme one week in the middle, so you get a breather, and apart from that, organise one day out and about, one day lazing at home or doing some home-based project like sorting out their rooms, making crafty stuff etc.
And head for the park every day, as you may bump into people that way.