Thacker was born in Okains Bay on Banks Peninsula on 20 March 1870. His father was an editor of the Sligo Guardian and after emigration to Christchurch in 1850, launched the second newspaper in Canterbury, the Guardian and Canterbury Advertiser.
Henry Thacker attended Boys" High School and then Canterbury College (what is now known as the University of Canterbury), from where he graduated with a Bachelor of Arts.
The newspaper failed after only a few months. He then enrolled at Edinburgh University where he gained his Bachelor of Medicine and Certificated Master diplomas in 1895. Two years later he gained a fellowship in the Royal College of Surgeons in Dublin.
Thacker returned to Christchurch in 1898 and opened a practice in Latimer Square.
He represented Canterbury in rugby union in 1889 and 1891 and assisted in the development of Richard Arnst. From 1899 he held the rank of Captain in the Army Medical Corps.
Thacker was the first president of the Canterbury Rugby Football League when the organisation began holding competitions in 1913. He served in this position from 1912 until 1929 and became a life member in 1920.
He was the manager of the New Zealand side during their tour of Australia in 1913.
The 1919 mayoral election was contested by Thacker, John Joseph Dougall (Mayor of Christchurch 1911–1912) and James McCombs (Member of Parliament for Lyttelton). Thacker contested the 1908 and 1911 general elections without success in the Lyttelton and Christchurch East electorates, respectively. He then contesting the Lyttelton by-election in 1913 as an independent Liberal, coming fourth with 5% of the vote in the first ballot.
He was re-elected in 1919 but was defeated in 1922 by Tim Armstrong from the Labour Party, when he came second out of three candidates.
In 1935, he was awarded the King George V Silver Jubilee Meda Thacker died on 3 May 1939 at Christchurch.
The Thackers had no children.
Thacker was a member of the Christchurch Hospital Board (1907–1922), Lyttelton Harbour Board (1907–1922), Christchurch City Council (1929–1931) and Mayor of Christchurch between 1919 and 1923. Thacker was a member of the Liberal Party and represented the Christchurch East electorate in the New Zealand House of Representatives from 1914.
