hi there are many laws which you could explore on this, but it will involve you taking the matter to a solicitor and it may cost a packet, thats why this thing happens everyday and people get away with it.
Here are the facts you are not the ownwer of the house and it's sold under your feed. You are not then intentioaly homeless and under the housing act the local authority where you are ordinarliy resident have a duty of care for you and the children. They cannot get out of that as its the law, even it they have no properties to offer you they have to find provision for you. It could be they house temporarily in a hostel of their choice.They may even offer you a property knowing you will turn it down, be carefull here as thewy could then discharge duty on you, which you would then have to appeal.
You need to gather as many points as you can, with doctors support, fleeing domestic abuse, makes you priority any disabilities are helpful. Avoid living with friends or relatives as you will not move forward and you are not considered a priory case as you have roof over your heads.
Remember housing departments are crafty and will not want the expense of temporary housing.
Shelter employ solicitors that are free you can make an appointment with them, but they will not see you if you already have a solicitor. Sheters solitors scare housing departments, so get them on board if you can.
Have you had a homeless interview yet or have you just applied for housing?
www.shelter.org.uk
Good luck keep in touch
Geoff.g.
