Meredith was born in Dedham in Essex in 1796, the only child of elderly parents who lived in West Ham. His father, Joseph Meredith, had been the superintendent of the local excise officers, but he was retired by the time of his son's birth. In 1804 aged 10 years Samuel Meredith ran away from his school at Greenwich and could not be found. He was eventually traced to a ship at Portsmouth where he had asked to be taken on as the cabin boy. John S. Dyer, a family friend who was Chief Clerk at the Admiralty and Secretary of Greenwich Hospital (and who would later become his father-in-law), obtained a position for Meredith as a midshipman aboard a ship in the Royal Navy. He then sailed to the Indian Ocean and did not return home until 1809.