Call again and ask for the persons name you speak to, as you are not in arrears or even pre-arrears the request goes to the very back of any queue.
You'll also struggle to borrow with one income and children because this reduces your ability to carry debt.
When we see cases like this it often ends with the person renting out their apartment and them renting out a house privately (I suspect it's part of what drove up some of the rental market growth since the crash, two renters forming out of what used to be one renter one owner).