In that case you need to go through all the things that indicate you might be cohabiting and sort them out.
That’s things like having someone stay over regularly, getting their post at your house, using your address for anything like bank statements, phone bills , insurance, having anyone pay towards your household bills or buying food shopping for you. This is even if they don’t live with you ( child maintenance doesn’t count ) and even if the children are not theirs.
Marital status is irrelevant - it doesn’t matter if they are married to someone else but living with you. Or living with / married to someone else and giving you money.
It doesn’t matter if you are “ financially separate “ but living together eg living with you for free. It will be assumed that they are contributing to your living costs.
If you have extra money coming in ( like a lump sum from an inheritance ) or change your working hours, you need to tell DWP.
You should have had a letter from DWP telling you that you are being Investigated and asking you for more info.
Yes your benefits can be stopped if they are sanctionable benefits.