Born in 1942 in Edinburgh to a Scottish medical family, he was brought up in Yorkshire, England, where his father, John, accepted a job as a surgeon on return from service in India during the Second World War.
After graduating from Cambridge he made an unsuccessful attempt to move into journalism before going on to study for an MA in International Relations at the London School of Economics.
In the late 1960s he abandoned academia in England and returned to Scotland, where he balanced his work at the University of Edinburgh with campaigning for the Scottish National Party (SNP).
His friend Owen Dudley Edwards, an Irish-born Edinburgh historian, remembers his press briefings as unique: "Hostile journalists were staggered to hear him explain that their objections to this or that in the party were not really rewarding subjects but that a more useful question to raise would be this other."
In 1979 Maxwell, together with Margo MacDonald, Owen Dudley Edwards and a number of younger nationalist activists (including Alex Salmond and Kenny MacAskill) established the 79 Group, a left-wing faction within the SNP.