[4] Parker was with his father at the Battle of Dogger Bank, and with Richard Howe in the two actions in the Straits of Gibraltar.

In 1801 he was appointed to command the Baltic Fleet destined to break up the northern armed neutrality, with Vice-Admiral Horatio Nelson as his second-in-command.

[6] At the height of the battle Parker, who was loath to infringe the customary rules of naval warfare,[6] raised the flag to disengage.

Famously, Nelson ignored the order from his commander by raising his telescope to his blind eye and exclaiming "I really do not see the signal " (although this is generally accepted to be a myth).

In Wilson's opinion "As an officer, Parker was an able administrator rather than a great leader and this was to prove a weakness when it came to having both St Vincent as his chief and Nelson as a subordinate"; and that "He was evidently a popular man for as Nelson wrote after Copenhagen:"[8] We all respect and love Sir Hyde; but the dearer his friends, the more uneasy they have been at his idleness for that is the truth—no criminality.

[10][11] His son Hyde, a captain in the navy, commanded Firebrand in the Black Sea, and was killed on 8 July 1854 when storming a Russian fort at the mouth of the Danube.