Absolutely know how you feel. This is exactly how it is for me too.
I work, but because I only do school hours and live a long way from work (an hour's drive) I very rarely get to socialise after work. And as I work through lunch I don't get to do any of the lunch time things either! So no mates through work. Not that any of them have any clue about how it is to be a single parent. Most of them don't actually have children either.
I fill up my free time doing voluntary stuff at school (helping on my day off, running an after school club, and organising school fetes etc). It gives me something to do but also a reason to chat to other parents.
I really don't know what it takes to get an invite to something social though. Trying to keep myself busy so I don't have time to reflect on how lonely and isoled I am.
One very kind mum offered to take my ds out for the day so I could catch up on stuff. She took him with a group of other mum's out for a fun day at a park about an hour away that I'd never been too. I really appreciated the free time to get stuff sorted, but I was also really wishing that I could have gone along for the social side of it too!
And yeah I've done the thing of not phoning or texting people to see how long it takes. Think the last time someone phoned me just to chat, not coz my sister needed a babysiter was probably at least 2 years ago. My two 'closest' friends didn't even text or phone me on my birthday (40th this year) though one did bring a card round a couple of days before.
It does get to be a vicious cycle though of trying to manage all on your own and putting on a brave face and everyone looking at you thinking you're doing managing fine and coping, when actually you're not at all, just simply getting by from day to day. Some better than others granted.
Sugarpear - I am essex, but a fair old way from the bridge (an hour ish). We could meet up somewhere in the middle though if you are able to drive maybe? How about Maldon prom and splash park for example?
desiretochange - If you're the other side of the water I'm guessing you're in essex too?