Born in London in 1806, Henry was the second son of Edward COCKERILL and Susanna BEELS. He had the benefit of an education but was convicted of stealing in 1823 and transported to Hobart Town on Phoenix in 1824. He was appointed to the Lieutenant-Governor's or Colonial Secretary's office as a clerk with a salary but was sentenced to 3 years hard labour at Macquarie Harbour in 1827 when he was caught altering the sentence of another convict. He was fortunate to have been useful as assistant clerk in the Commandant's Office there and left there for Bothwell in 1829 where he was a clerk in the police office.
By 1831 he was settling down, with some land, a garden and a house commenced. In 1832 he sought permission to marry, but already some in Bothwell were objecting to him. He married Eliza VINCENT that year and received his conditional pardon in 1836 so he was able to leave his position as a clerk and become licensee of his father-in-law's inn. They had 15 children with only two dying as children.
In 1841 Bothwell was rocked by an attempt to rescind his recently approved membership of the Bothwell Literary Society. By 1843 he was seeking to give up innkeeping and obtain a position with the government, with an eye to the future of his children.
The family moved to the New Norfolk area in 1851 and may have tried farming. They were living at the Cawthorn property Arundel at Macquarie Plains in 1864 when his wife died.
Eighteen months later, he remarried to Alicia CORRIGAN, the widow of Dr Kenneth MaCLEAY who had been at Bothwell in 1848.
Henry died in New Town in 1873 and was buried at Cornelian Bay.
Janet Miller, one of his New Zealand descendants, wrote a COCKERILL family history in 1994.