Lodger status question

Hello - I would appreciate some advice please.
Some time back I had to move out of my rental place. I found a new place to go to but there was a 'gap' to wait out b4 I could move in.
A friend took me in for what we thought would be a few weeks to a month. He is my Ex-husband. (We divorced over a decade ago, lived separately ever since, remained friendly).
Fast forward 2 months and the new place falls through. I live in a popular county. It is very difficult to find rental property.
We told the DWP/HB straightaway that I was now staying at friend's place temporarily while I looked for new accom (which I have been doing but no luck). Obviously concerned how this could all affect him as he receives pension credit/HB and pays no council tax (he is over 70). I receive the support portion of ESA as I have ill-health but some savings. I am 57.
He explained the situation to the Authorities ie that I am effectively homeless , so he is helping me out and that I am not paying him rent. Also let his Council know (he lives in a 2 bed sheltered house). They referred to me as his lodger and he said no I am just a friend he is helping out. He gave me his bedroom and moved onto day bed in the lounge (he uses the smaller bedroom for his studio). So more time goes by and we have now heard from the HB office to ask am I still living with him.
My worry is that they will say we are a couple and then try to make me pay for everything. We are not a couple, we sleep separately. We have our own cars and bank accounts and all we share is the house space. We are like a brother and sister living together or 2 friends but my memory of this kind of arrangement is that 'they' won't believe us and suddenly I will be on the hook for paying all the CT/rent and topping up his pension too (as its not fair on him to lose out because of my problem finding somewhere new to live). Can you advise us please?

Hi saz, another source of advice is Shelter:
england.shelter.org.uk/get_help
they say many questions can be answered using their website, but do have a phone helpline if you can't find out what you need to.
As with some other situations, I would keep receipts for all sorts, eg your shopping, car bills [insurance, MOT etc] so you could prove your independence if you had to. A good way to store such flimsy things is staple them into an exercise book as you go. This way you can write next to the slip of till roll what it was for, if it is not itemised. A bit of a nuisance I know, but better do it, than wish you had later if you hadn't!
Best wishes,
Denby

Thankyou, I have not registered homeless no. I am not sure where I would do that. Do you know?
I dont think I would be eligible to register for the Home Choice scheme as that is for when you have savings less than 15k and right now I have more than that.

So it sounds like it is better to say I am a lodger than a friend? Because otherwise they will try to make out we are a couple, which we aren't, and then make me pay for everything....will look into the CAB appointment service but COVID has got everyone shut down of course....