Dacres was born in 1804, the son of Captain, later Vice-Admiral, Sir Richard Dacres and Martha Phillips Milligan. The Dacres had a long history of naval service, Sydney's uncle, James Richard Dacres, was a vice-admiral, while his cousins Barrington Dacres and James Richard Dacres would both serve in the navy, the former becoming a post-captain, the latter a vice-admiral. His father, Richard Dacres, had served with Sir Sidney Smith as his flag captain aboard HMS "Pompee" during his Mediterranean campaign, and under Captain Sir John Colpoys, while Colpoys was commander of and . His elder brother Sir Richard James Dacres was a general in the British Army and was also awarded the GCB.