Born to a family from Devon, by around 1804 Teed was established as a ship agent, banker, and merchant in Plymouth.
In 1806 he unsuccessfully sought election to Parliament from Fowey, a rotten borough in nearby Cornwall, along with Admiral Alexander Cochrane.
Teed ultimately deserted the Hawkins interest and was elected anew in 1812 with Andrew Cochrane-Johnstone, serving until 1818.
His son John Godfrey Teed (1794-1871) became a barrister at Gray's Inn, Queen's Counsel, and a judge of the Lincoln County court.
Henry Cowd Teed (d. 1831) married Frances Marie, a daughter of jurist William Rothery, in 1823, but she died the following year; in 1829 he remarried to a woman named Maria Robertson.