In 1966 he made his debut for England against Ireland at Twickenham. In total he won five international caps until 1969,[2] serving as captain in his last game, again against Ireland.[3] He never won a game for England, drawing one and losing four.[4]
In 1973 he was sent to Kenya by the Rugby Football Union on a coaching assignment, and while there was selected to play for The Scorpions, an East African invitation team. After this assignment he moved to Italy to play for Rugby Roma from 1973 to 1976,[5] becoming the Italian Championship's best try scorer in 1974 and 1975. So enamoured had he been by his time in Kenya that he persuaded his Italian club to tour East Africa in 1976.
After retiring from playing he coached Preston Grasshoppers. He was coach of England from 1983 to 1985, an unsuccessful period for the national team.
He remained president of Waterloo after his retirement. He is also involved in rugby league, serving as chairman and coaching the junior sides of Prestatyn and Rhyl Panthers since 2011, and is (as of 2015) on the board of directors of Wales Rugby League.[6]
Outside rugby, Greenwood was the Assistant Bursar and a geography teacher and head of rugby at Stonyhurst College.[8]
Greenwood and his wife Sue have three children: one daughter and two sons, one of whom is Will Greenwood, who also played rugby for England. Sue is a retired teacher who taught mathematics at Stonyhurst St Mary's Hall for over two decades.
Greenwood caused embarrassment for Preston Grasshoppers Rugby Club in November 2021 when he arranged for Nigel Farage to speak at a sportsmans dinner at the club. When the club found out that the divisive former UKIP leader and Brexit campaigner was speaking, they cancelled the event. However, the story was covered widely by the national press after members tweeted that they were cutting up their membership cards in protest at the club being associated with Farage.