In the following note, I believe "his father" is the Thomas Player referred to:
"Player was the grandson of a linen draper in Canterbury. His father was captain in the trained bands sent by Parliament to the relief of Gloucester in 1643, and became Chamberlain of London for life in 1651. He and his father were knighted together by [Charles II] in recognition of his father’s services in the collection of the loans granted by the City to the crown at the Restoration."
(The biographies for 1640-1660 are still being written, so hopefully more info. will be available soon.)
Chart showing the number of references in each month of the diary’s entries.