I'm not a single parent but used to take DS alone when my husband was away in the army.
I loved it actually, and we still do have trips away together.
We've done the Haven sites, had a blast in Blackpool but they can be quite pricey. But you can drive which takes the stress off travel arrangements, and cater for yourself to keep costs down. The downside is that you are still clearing up, washing dishes, making food etc. so not a big rest for you.
I'd look at an all inclusive Family Village type set up. I know a lot of people are
at others using kids clubs and can be very judgey, but when you have no support network, spend night after night in your house catching up on chores etc then you deserve a break.
The activities they have these days are great - swimming lessons, football camps etc. The little ones are out of the heat and you get a proper rest. The price of the holiday is upfront, and it's easy to budget. You can do as much or as little as you want, no clearing up, no cooking, bed making etc
Plenty of people around to either talk to, or blend in around if you want peace. Balcony to sit on with a nice glass of wine and a good book when the kids are in bed. 
We also do the Premier Inn short trips - great value and you'd get a good deal with breakfast as kids eat free!