Anstey was born in Kentish Town, London, a member of an old Devonshire family. He went to Hobart, Tasmania in 1827, where his father was one of the first private settlers, renowned for his role as a magistrate and councillor and for the efficient management of his large livestock business.
In 1846 Anstey resigned his fellowship to devote himself to politics. After denouncing the arrest of William Smith O’Brien for refusing to serve on a parliamentary committee, he assisted the repeal candidate, Anthony Flaherty, in petitioning the result of the Galway by-election of February 1847. On O’Brien’s recommendation, Anstey was brought forward for Youghal at the 1847 general election and was returned as a committed repealer.
Anstey never missed an opportunity to ventilate his views on colonial, Irish and Catholic affairs, such as when he attempted to thwart Palmerston’s plan for British diplomatic relations with the Vatican.
Anstey was a formidable debater, who was said to have ‘not only command of language, but a sinewy facility of both speaking and writing … besides a curious power of pertinacious sophistry, which was difficult to meet even when he was most wrong’. However, his willingness to speak upon almost every subject that came before parliament, including Indian affairs, the government of New Zealand, the condition of Poland, sugar duties, Arctic exploration, and the use of chicory in coffee, won him few admirers in the Commons.
In divisions on foreign policy, Anstey voted with Russell’s ministry on its Australian colonies government bill, but sided with the Conservatives over the administration of Ceylon in 1850. Palmerston was said thereafter to have taken ‘the trouble to convert him from an enemy into an ally’ and Anstey subsequently ‘gave sincere concurrence’ to the foreign secretary’s policies (at least ‘since February 1848’) during the ‘Don Pacifico’ debate that June.
At the 1852 general election, ‘the omniscient member for Youghal’ abandoned Ireland to contest Bedford. Never having been an opponent of the established church, he now denounced the Catholic hierarchy’s involvement in Irish electoral politics and, with characteristic independence, campaigned for the repeal of the Maynooth grant on the ground that it was ‘inexpedient to give support to religious establishments out of the resources of the state’.
On 9 October 1855, Anstey was appointed attorney-general for Hong Kong and, in May 1856, became a member of its legislative council.
