On another note, I had no idea you could get £560 in benefits when earning an average salary. OP, Do you get all the other entitlements too, like free school meals, reduced council tax, bus passes, grants for 16 year olds, possible grants for your children at university, free prescriptions, free dental care etc etc. If so, I might get to the job centre to see if I am entitled to UC. I never even realized I could on an average wage. We can’t afford to live now, let alone when / if my kids go to university. I take on extra work when possible, do surveys, sell on Vinted etc.
The OP & the many other women whose stories you read on MN are only entitled to a top up since their rents have spiralled up out of all proportion to wages. That's the big problem: The cost of renting.
So if you want to need a good wage supplemented (strange ambition but whatever), you need to arrange to pay a very high rent and not have a partner. Personally, being thrown back into the rental sector, in this economy, is literally the stuff of my nightmares, but you do you.
Working UC recipients don't get free school meals, free prescriptions etc unless they are on a tiny part time wage. Full time workers such as OP could never qualify for those things. Sorry. I expect that's a blow to your plans.