On your probate form you declare the full value of your dad's estate. In this case the vslue of the house , lets say £150,000 plus £31 in the bank. He received lets say £200 from the DWP which is an advance payment and has to be refunded. In addition, there is the cost of the funeral, lets say, £3000. As your dad's estate is so large you will not get a funeral payment. They may pay the undertaker then put a claim against his estate. There are rules about the order that debts have to be paid when someone dies and you are an executor of the estate. Total of his estate is £150,031 less debts of £3200, means value of the estate is £146, 831 (less than the value of the house).
You have 2 options. Sell the house or pay off the debts. Any creditors are entitled to payment FIRST and are not obliged to take payment in increments, especially when there is value in the estate. You may need to take out a bank loan in order to pay people off in full. If you say you have no money, are you on benefits? How will you be able to afford the running costs of a home if you're skint? Another option may be to release some of the equity in the house. You say they can't get blood out of a stone, but they can. The house cannot transfer to you until all the debts are cleared.
Finally, have you searched to see if there are any insurance policies that you didn't know about? Some might be paid up for example?
Fiona