Son of Prime MinisterJ. M. Andrews, he was educated at Moure Grange Preparatory School, County Down, and Shrewsbury School. Andrews entered Parliament as MP for Mid Down in 1953 (replacing his father), a seat which he represented until his resignation in 1964, when he was elected to the Senate where he sat until the Parliament was prorogued in 1972. His election to the senate was following a cabinet reshuffle, in which Andrews accepted demotion to the politically unimportant position of Government Minister in the Senate.
He held several Cabinet positions, including Minister in the Senate from 1964 and Deputy Prime Minister from May 1969. He was a contender for the position of Prime Minister on the retirement of Lord Brookeborough, but when it became clear that Terence O'Neill had a comfortable lead over both Andrews and Brian Faulkner in the parliamentary party, no contest was held. In 1969 he was approached by O'Neill to succeed him, but he refused and James Chichester-Clark was elected
During the 1970 Bannside and South Antrim by-elections, Andrews was at the centre of the UUP's pluralist campaign against Ian Paisley's Protestant Unionist Party, declaring "What does Protestant Unionism mean? Does it mean that you have to put a sign over the door of the Unionist Party saying Protestants only?"