How do I close my late DFs Post Office Book?

Sorting out some old paperwork and effects from my late DF I've found a PO savings book, amongst photos we kept in the loft.
It's years old as he died in the late 80s. I was NOK so registered the death, paid for funeral etc. He had no money or anything worth anything when he died. Was in a council home for elderly who gave me £3.50 of his money. So I was really shocked to find a balance of £15 in the PO book.
I've sent for a copy of the death certificate but who do I send it to?
As it's almost 40 years ago now I don't have any other paperwork.
Any help on this would be greatly appreciated
Thanks