I'm a single mum, too.
But I'd be worried if after tax, mortgage/ rent and bills I only had ~£1k per month left.
That would then need to cover food, commuting, clothes, days out, school trips, Christmas and birthday presents, holidays, prescriptions, any extra curricular activites and transport there and back, car maintenance, house maintenance, replacing old appliances as they die, school uniforms... etc
I realise some of those are optional, but many aren't and I'd be worried about even covering the important ones for kids to have a good life with that budget. I also realise many do that because they have no choice, and sacrifice all but the very essentials. But even those would be hard to squeeze into £1k, especially with energy bills and tax rising so shortly that figure could easily be £700 or even less.
Just because you've had to scrape by before (I have too!!) is not a reason to tell the OP that it will be easy on that budget. It won't. Any curved ball like a broken washing machine or boiler or MOT requiring a lot of work on the car etc could put her into a very difficult situation.
Personally OP I'd try to find somewhere with a cheaper rent to give yourself more breathing space in the budget. There is nothing worse than worrying about how you will pay your bills. The next couple of years are going to be very tough financially for everyone unless you are exceptionally lucky so you need some slack in the budget, IMO.