Sir Arthur was the proprietor of the Portsmouth Times, founder of the Southern Daily Mail and the Hilsea-based Holbrook Printers, a deputy Lord Lieutenant and later Conservative MP for Basingstoke.

In 1903, he enrolled in the officer training establishment Britannia Royal Naval College and was appointed midshipman on 9 January 1905.

[2] Holbrook was 26 years old, a lieutenant in the Royal Navy during the First World War when on 13 December 1914 at the Dardanelles, Turkey, he performed a deed for which he was awarded the Victoria Cross.

Notwithstanding the difficulties of a treacherous current in the Dardanelles, he dived under five rows of mines and torpedoed and sank the Ottoman ironclad Mesûdiye, which was guarding the mine-field.

On 24 August 1915, amid a wave of anti-German feeling related to the First World War, the name of the New South Wales Eastern Riverina town of Germanton was changed to Holbrook to honour the recent VC recipient.

Holbrook's medal group, including his Victoria Cross, went on display at the Australian War Memorial on 11 December 2009.