He joined the Territorial Army in the King's Royal Rifle Corps and during the Second World War served in Italy and Greece as well as at the Staff College.
He was demobilized early as a Parliamentary candidate, fighting South Ayrshire for the Conservative Party in the 1945 general election.
He fought the same seat in a 1946 byelection, having in the meantime been elected to Chelsea Borough Council for Hans Town ward.
Mathew was chosen for the safe seat of Honiton and won it in the 1955 general election.
Derek Walker-Smith, who served as Minister for Health, picked him as his Parliamentary Private Secretary from 1957 to 1960 and also in 1964.