Mary
You need to contact the DWP office dealing with your ESA claim as soon as you sell your existing property, any equity should be disregarded for 26 weeks, if it looks like you will exceed this then contact them again, a DM can extend the period but you will need to show that you are actively looking for a new property and why you have not been able to purchase.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems