Hi I hope I can help, I work in social housing!
The long and short of it is, if you have given up your home volunarily (you dont like an area had enough/ or you got repossessed due to non payment of mortage rent etc) then you are Intentionally Homelesss, the problem is that given the ages of your children, they are all classed as adults! If they were all under 18 then there is a duty under law as they protected under social services legislation. They could each make independent housing applications in fact!...as long as they can demonstrate a vulnerablity under the Housing Act 1998. In fact they may insist you do this as its easier to find 1 bedroom flats to rehouse people in that 3/4 bedroom houses ! (due to shortages!)
Your financial situation will have a bearing on your application, as the LA will take into account that you can ill affod to rent in the private sector. But it will depend on other factors such as the effect this may have had on the familiys health etc
As such your application will be proceesed, each LA works diff some work on points some work on priorty banding (High priorty to low priorty) after you application is assessed you will be advised where you are on the list - you can challenge this with doctors letters etc. If you are not accepted as being Stat homeless.. you have 28 days to appeal the decision.
You qualify for emergency accomodation, in the event you lost your rented tenancy , It would intially be B&B accomodation and then a temp flat.
To be honest where you are in the country will be a factor, in terms of the avaliablty of social housing! and the demands upon it!
If you want more info in more depth let me know!
I would recommend that whatever the outcome of your applciation you go to CAB for more advice, especially if you have to appeal their decision
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