Puckey was born in Penryn, Cornwall, and christened there on 5 June 1805. His parents were William Puckey senior and his wife, Margery (née Gilbert). William senior, and his brother James Puckey, had been in the original London Missionary Society (LMS) party that travelled out on the ship Duff, and attempted to establish a LMS mission in Tahiti in 1796, but when that mission failed, went on to Paramatta, Australia. William senior returned to England about 1802, married Margery Gilbert and had 4 children. The family left England in 1815 for Australia, and in November, 1819 William Gilbert and his sister Elizabeth, (later to marry Gilbert Mair) came with their parents to Kerikeri, New Zealand on one of Samuel Marsden's missions.