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".