Ok. 33 years in Fraud so hope I can give you a reasonably clear answer on what they are looking for.
First of all I want to expel a myth. (Because it's used as a defence EVERY time) 'he doesn't live with me and only stays over x times a week'
There is NO specific amount of time if he has another home. This is ALL about lifestyle.
'Living together' is an offence . (Actually the offence is failure to notify a chance of circumstances, if you have got together since claiming to be single OR false representation if you were already in a relationship when you claimed)
Anyway.. it might help to understand WHY this is an offence.
If you claim as a single person it is assumed you have no additional income with which to run your household above that which you have declared for yourself. Every year the government legislates an amount of money the state should give you to help you support you and your family.
So for example . £500 rent (depends on area) £330 ish for you and £250 ish per child and then any money you earn is deducted after an allowable amount. (CMS is not counted) Out of that you are expected to run your entire household.
So compare yourself to say your neighbour who has no partner . Imagine you were in an exact same position. Both have 2 kids. Same rent. Same council tax. Same utility costs.
Now ask yourself . Does your partner contribute to your household ? Does he buy groceries for the family ? Does he pay the tv subscription? Does he pay car or travel costs for you ? As a very occasional thing (ie buys a takeaway at the weekends ) this wouldn't matter. However is it a regular thing.
Because it's obviously not fair if you have some or any of those things paid for you regularly when you neighbour in the same boat doesn't get that. It leaves you with more disposable income because you have a partner.
Now you can see what they are going to ask.
Unfortunately most living together allegations are made by friends family or neighbours because they feel it is unfair.
I had a case a few years ago where the partner literally paid for everything and the benefit money was the womens 'pocket money' . She was incandescent with rage because her boyfriend had another home where he paid his own council tax.. just would not have it that she was doing anything wrong. (Had three kids with the man between claiming and the court case !)
They will also ask about how others regard you. ie if neighbours/friends see you as a couple. In the case above it was the woman across the road who made the allegation although the convicted woman would never be privy to that information. (She was also a LP on benefits)
My advice would be to be honest and say if he makes regular contributions in any way. If he doesn't then say that. You can also ask for a publicly funded solicitor to attend with you if you wish.
Last but not least it is important to understand that 'under caution' includes your right to refuse to answer questions. However that normally means we have no other choice but to dig deeper. It is still your right though.
I hope that assists to put you in the picture ?