Eddie was signed up as a 14 year old and was brought on at Tottenham Juniors and other nursery clubs Spurs used to hone the talents of their youngsters before bringing them into the senior set-up.  He spent time as an amateur at Finchley before being called up for service in the Second World War.  Spurs did not maintain his registration, as they had mistakenly believed he had been lost in action.

This meant that when he returned to England in 1945, he found himself without a club and was signed by Chelsea.  When the player was found to be at Stamford Bridge, Spurs explained the situation to Chelsea and they released him to return back to White Hart Lane.

He was a major player in the Arthur Rowe "Push and Run" side of 1949-51, which took the Second Division and the First Division titles in successive seasons.  His energetic and confident play was an integral part of the team's style and it brought him to the attention of the England selectors, who picked him nine times for the national side in the 1950s.  His dynamic runs and accurate passing made him a pivotal figure in the Spurs midfield and his reliability meant he played every game in the three seasons around the two title successes.

During the league programme either side of the war, Baily played 325 competitive games for the club, netting 69 goals.

During his time at Spurs, Eddie won nine England caps against Spain (1950), Yugoslavia, Northern Ireland and Wales (1951), Austria (twice), Switzerland and Wales (1952) and Northern Ireland (1953).

He left Tottenham in January 1956 to join Port Vale, where he stayed for nine months, playing 26 league games and scoring eight goals.  From Vale Park, he moved to Nottingham Forest, helping them to regain their First Division status, then on to Leyton Orient where he also began coaching and once more spurred the club he was at to rise to the top flight.

Returned to White Hart Lane in October 1963 as Bill Nicholson's assistant manager, where he led Spurs to a successful period of the club's history at home and in Europe.  Always a stern taskmaster with his players, he still held the belief in the "Tottenham Way" that was a trademark of the teams he played for and coached.

Eddie left in September 1974, before moving on to West Ham where he took on a back-room role doing some scouting before retiring to live in Hertfordshire.  During his time after Spurs, he was a PE teacher at Bishops Stopford's school in Enfield.

He was awarded a testimonial game, which originally was to be against West Ham United, but they were too busy to fit a game into their schedule and a local match at Enfield was arranged.  It looked as though this would not realise too much money for Eddie, coming on the eve of the FA Cup final, but on the day of the match, manager Terry Venables was sacked by Alan Sugar and a big crowd attended at Southbury Road to watch the game, voicing their views on the news that broke earlier that day and Eddie was the main beneficiary of Venables' loss.