Cobcroft was the son of parents from the Sydney suburb of Summer Hill.[1] He attended Sydney Grammar School and represented the school in football, rowing and running.[1] He also played for Newtown in the Sydney Rugby Premiership as a full-back. After leaving school, he moved to Fiji in 1907 to work on the sugar plantations of C.S.R.[2][1] He moved to Western Samoa in 1911 to manage Papaseea Plantations, and became manager of the Mulifanua Coconut Plantation during World War I.[1] After a brief stint working in the Territory of New Guinea, he returned to Western Samoa and established his own cocoa plantation.[1] He became President of the Planters Association and Vice President of Apia Turf Club.[1]
Cobcroft contested the 1932 elections to the Legislative Council with the support of the Chamber of Commerce and the Planters' Association. He was elected alongside his brother-in-law Irving Carruthers.[1] He unexpectedly lost his seat in the 1935 elections, receiving the fewest votes of the four candidates running for the two seats.[3] The following year he was amongst the founders of the United Progressive Party, becoming its first chairman.[4]
He died on 5 September 1955 in Auckland at the age of 70.[5]
