Homeless with 2 children

Due to circumstance beyond my control my children and I are currently living in emergency accomodation. We are in a B&B which consists of 1 room. 
I have no family as I was brought up in care and no friends able to help.
We have been told by the council that becasue I was in rent arrears before I lost the house (Even though I was paying this off with both parties being happy) we could be found intentionally homeless.

The reason for this is because I work and claim universal credits, They have never got a payment right yet, leaving me unable to pay all the rent leading to the eviction, but becasue I was already in arrears the courts granted the eviction.
We have lost all our furniture and 50% of our personal belongings as was unable to come up with funds for storage or have anyone to help.

We will be looking for private rented accomodation as this is the only option. We are currently trying to get as much money for a bond which would be £500-700 minimum, A months rent upfront, again £500-700 minimum and we will need the basics furniture wise to get started.

We have 4 weeks from today to raise the funds and find suitable accomodation or my children will be rehomed and I will become intentionally homeless.