Early career (1970–1983)
Henderson became a supporter of Scottish independence at an early age, and joined the SNP aged 14. He was President of the Edinburgh University Nationalist Club. Henderson became heavily involved with the SNP after he returned to Scotland from South Africa in the mid-1960s. He was also the director of programmes for Radio Free Scotland from 1963 to 1965, and was Senior vice-chairman (depute leader) of the SNP from 1970 to 1972,. He was selected as the SNP candidate for East Aberdeenshire in 1972, and moved to live in the constituency, developing links with local fishermen, farmers and businessmen. He was elected at the February 1974 general election, and re-elected in the October general election later that year. The SNP were in the ascendent, campaigning on the basis of "It's Scotland's oil".
Henderson served as the whip and was a leading member of the group of 11 SNP MPs in the House of Commons. In 1975, he negotiated a position for the SNP's Winnie Ewing in the British delegation to the European Parliament, where she became known as "Madame Ecosse". He was later the SNP spokesman on employment and industry. He was instrumental in the SNP's decision to lay down a censure motion in the House of Commons, criticising the Labour government of James Callaghan after 1 March 1979 referendum vote on Scottish devolution failed to be approved by the required 40% of the electorate. At the time, the Labour government were reliant upon support from the SNP. The motion was carried by one vote on 28 March and Callaghan immediately called the general election which brought the Conservative Party led by Margaret Thatcher to power. Callaghan described the actions of the SNP as "turkeys voting for Christmas". Henderson lost his seat to Conservative Albert McQuarrie in the 1979 general election by less than 600 votes, and only two MPs from the SNP remained in the new Parliament.
He returned to his business career, but with less success than the 1960s. At the SNP Conference in 1979, he was elected the party's Senior vice-chairman (now described as deputy leader) (to leader Gordon Wilson), defeating Margo MacDonald for the post. He remained in this position until 1981, when he stood down on health grounds.
He fought the new seat of Banff and Buchan, which had largely replaced Aberdeenshire East in the 1983 general election. He again lost to Albert McQuarrie by less than 1,000 votes. The 1983 election saw the SNP only win the two seats that they had held in 1979, but Banff and Buchan was one of three that they came close to recapturing from the Conservatives. Future SNP leader Alex Salmond would win this constituency from 1987, and it would remain in SNP hands until 2017. Henderson also suffered in his private life, being divorced in the early 1980s.