What do I tell the council and put down an address for work?

I haven’t been able to find anywhere to move to. I had move out the house yesterday. At the moment I’m staying between places. A few days a week I’m staying at my mums house and a few days a week at my aunties house.
Until I find somewhere to live. So I’ve put all my stuff in storage.

The house was private rented and I’ve lived there for 11 years.

The problem is what do I tell the council because my mum is on various different benefits including housing benefit and she’s on disability and so is my auntie.
At the moment I’ve not got a main address but I work full time so
I have tell my work, the council and I don’t know who else where I’m living.

I don’t want my mum to lose her benefits and at the moment she’s getting a single person council tax discount.

My mum is on DLA, ESA, housing benefit, severe disability premium, council tax reduction

I don’t want her to lose her benefits
I don’t know how long I’ll be staying with my mum and auntie. My auntie is living in an over 55s housing complex so I can’t stay there for too long. I’m not supposed to be staying there anyway.
I also have a dog.

What should I do
What do I tell the council about where I’m living?

Thanks in advance