My mum died a few weeks back , I have had a letter from her housing association to say she must give 4 weeks notice and that the 4 weeks rent comes to just under 800 pounds but she never had any money when she died , can they take me to court to get the money off me as they said they will

NO. Her estate is responsible for her debts. If there was no money left, then you send them a letter to that affect. You are not responsible. However, you cannot take any money from the estate until whatever was left is used to pay her debts.

Did you tell them that she has passed ? Under those conditions its unreasonable if not impossible to say 4 weeks ahead. They are nuts.

NO. Her estate is responsible for her debts. If there was no money left, then you send them a letter to that affect. You are not responsible. However, you cannot take any money from the estate until whatever was left is used to pay her debts.

I agree but this 4 week notice rule does not apply in a case like this. The contract ended with the passing of the party. Its no longer valid.

Good point. They really can't apply a notice period when the tenant dies.