DONT close the accounts yet, you may need to pay money out from them, or pay money IN to them (if an organization like the Gas board etc owes the person who died money).
The bank will happily pay for the funeral out of one of the accounts if you ask them.
My wifes mother died a few years ago and my wife closed the bank accounts and then had all sorts of problems when she got cheques BACK from people like the gas board, written out to her mother, but she had no acount to pay them in.
Took a while to sort out.
Close the accounts down near the end when everything has been sorted out.
Maybe buy a small book about being an executor of a will to help you.