Have a look at the Money Helper Budget plan. Look at how much your income will drop when the UC stops. And what you will save on energy/food costs/etc when the kids aren't there.
You may find that you can manage, or maybe downsize and still have a room they can come home to. Rent somewhere where you can put a spare bed in the lounge, for of they are home the same time.
I will be in the same situation in a few years. Or maybe even next year if the youngest leaves school at 16.
It boils down to them needing to contribute to the household. And unfortunately if we are not in a position to support them, that's what will need to happen.
I'll also be looking at a lodger/airbnb one of the rooms. This is more difficult if you rent, but even foreign students may be an option.
It pisses me off that I'll be in this situation. My ex husband benefited from me raising the kids while he excelled in his career. I've had to manage a challenging ASD/ADHD child, and adapt the job thay I do accordingly. But it's about future planning, and downsizing if needed.
It'll do the kids good to learn to manage their own money, and to realise they need to pay their way.
Edited for typo