Mum's leaving home, help ?

You can stay as long as your name is on the rental agreement mainly because income support will be paying a contribution to your rent You must go speak to the council and DWP. The council will give you some help with your council tax but the rest of it comes from income support. If you do have to leave the council will give you no help in finding other accommodation they may arrange to put you up in a hostel or temp accommodation. You do not need to inform the council if you rent out the room but you do need to tell DWP as any money you get is cled as income and will effect your payments