Born in Cleator—then in Cumberland—Graham studied at the Workington Technical School.
He started work at 16, and immediately joined the Amalgamated Engineering Union.
He studied with the London University External System, and served with the Royal Air Force during World War II.
After the war, he held a variety of engineering jobs, and also worked for the Workers' Educational Association as a tutor at the University of Southampton.
[1] Graham joined the Trades Union Congress in 1961, rising to become head of the organisation department by 1966.