During World War II he served in the Royal Air Force in Northern Ireland and guested for Belfast Celtic.

[8] After three years at Brentford, he returned to Chelsea, where he played 66 times and won a First Division winners' medal in the 1954–55 season under Ted Drake.

[10] He was never capped for his country, though he did make a single 'B' team appearance, whilst at Brentford, in a 1–0 victory against the Netherlands on 23 March 1952 at the Olympisch Stadion in Amsterdam.

He coached Eastbourne United, Oxford University (where he came to the attention of Sir Harold Thompson, a future Chairman of The Football Association), and England youth teams.

He remained there until April 1961, when he was selected by chairman Reg Pratt to replace Ted Fenton as manager of West Ham United.

West Ham's league form under Greenwood was less impressive, usually finishing in the lower half of the First Division table, though they did come sixth in the 1972–73 season.

When West Ham played Birmingham City in a Premier League fixture on 13 February 2006, a one-minute silence was held in Greenwood's memory.

[17] The Heritage Foundation charity erected a blue plaque in Greenwood's memory at West Ham's Upton Park, which was unveiled by his family on 21 January 2007.