Cox was educated at Eton College, where he was a good friend of his contemporary Quintin Hogg, later Lord Hailsham.
Trevor-Cox was the Conservative candidate for the North East Derbyshire constituency in the 1935 general election, but lost to Labour's Frank Lee.
In April 1937 he contested the Cheshire constituency of Stalybridge and Hyde in a by-election and won, with a majority of only 334 votes over the Labour candidate, Rev Gordon Lang.
He was appointed in 1938 as a Parliamentary Private Secretary to the Trade minister Ronald Cross, becoming the most junior member of Neville Chamberlain's government.
He stood unsuccessfully as the Conservative candidate for Birkenhead in the 1950 general election but otherwise concentrated on his estates in Wiltshire.