How big is the house? How many bedrooms, does it have a dining room and how old are your DC (can they share, maybe even with you and save space?)
I'm wondering if you might have space to take in a lodger, as you can do that without it affecting your Universal Credit.
You would need to check your lease allowed it also.
www.citizensadvice.org.uk/housing/renting-a-home/subletting-and-lodging/lodging-index/taking-in-a-lodger-what-you-need-to-think-about-first/
We used to do this when my DS was young and it really helped.
Mumsnet is very anti-lodger, half of the people here are aghast at the notion of having guests to stay, let alone sharing your home with someone on a long term basis!
Mumsnet will also tell you that lodgers don't want to live with DC, but that's also not true. There are lots of people who need low cost housing who don't mind loving with DC.
If you aren't against the idea personally, it can be a godsend IME.
If this is a possibility, my tips would be, don't just take the first person who wants a room, you're basically interviewing people to be a part of your family temporarily, so try to find someone you'll get on with, don't move anyone in you think may be incompatible. Take your time to choose the right person.
Check out their social media and web presence to look for signs you'd be incompatible. (We rejected two lodges who'd seemed really nice after checking out their internet presence. One was a racist, the other a loopy religious fanatic).
Be very honest about what you are like when you talk to them, eg if you are tidy / messy / sociable / introverted, so you can find someone compatible.
With DC in the house, and you being single, personally I'd only consider moving women in. Men are just too risky IMO.
Do you have a uni in your town? We used to rent to mature students. This meant they were there for a reason, stayed for about a year and then left, so if we didn't get on with someone brilliantly, we knew they were leaving anyway so it was no big deal, we could muddle through. This worked well for us.
If you take a deposit for breakages, you have to put it in a tenant deposit scheme. This is a good thing as you won't be tempted to spend it!
We didn't take a deposit for breakages. Instead, we took two months rent when they moved in, the second month being their last month's rent. This meant that when they gave their month's notice to leave, they'd already paid for that month, so they simply didn't pay that last month. This protected us against people just leaving without notice and not paying the last month, so we could use that time to find their replacement and not be out of pocket. It suited them too as they weren't tied into a fixed contract.
The extra money was incredibly helpful and we even made some life long friends as a result. You get to know each other very well living together!