His father was a ship's rigger and upon leaving school, he was apprenticed to Fairfield's yard on the River Clyde before becoming a fitter at the Rolls-Royce plant at Hillington in 1953.
In the runup to the 1987 general election, Dunnachie was selected to follow James White as Labour candidate for Glasgow Pollok by 50 votes to 41 for Dave Churchley.
Initially he declared his intention not to pay his Community Charge (or Poll Tax) although he was never prosecuted for the offence, and observers have concluded that he must have decided not to fight.
His Catholicism showed in votes in favour of Bills which restricted abortion and against any lowering in the age of consent for homosexual sex, and he also opposed a deregulation of Sunday trading in 1993.
This move made the selection in Govan much more open and eventually doomed the chances of Mike Watson who was the sitting MP for Glasgow Central, the nomination going instead to Mohammad Sarwar.