Educated at Bedford School, Milne began his architectural training in 1898 when he was articled to Sir Arthur Blomfield. In 1902 he joined the office of Sir Edwin Lutyens. In 1904 he set up his own practice and in 1919 formed a partnership with Paul Phipps.
Amongst Milne's commissions in London were the interior of Claridge's Hotel and the Eleventh Church of Christ Scientist, Baker Street. He was responsible for buildings at Bedford School, Blundell's School, Cheltenham College, Christ's Hospital, Dame Alice Harpur School and Highgate School.
He was Vice-President of the Royal Society of Arts between 1959 and 1961.
He died on 15 January 1968, aged 86.