The office of Lord Admiral, later Lord High Admiral, was created around 1400, and was the title given to the head of the Royal Navy. From the 17th century onwards, however, the Navy was commanded by a committee known as the Board of Admiralty, so that the title Lord Admiral was no longer given to any one individual.
The members of the committee were known as Lord Commissioners of the Admiralty, Naval Lords or Sea Lords. From 1806 onwards, it became customary to appoint a civilian as the First Lord of the Admiralty (the leader of the Admiralty Board) at which point the title First Sea Lord was given to the most senior Royal Navy admiral. Presumably, William Price is referring either to the First Lord of the Admiralty or to the First Sea Lord.