Defender Spicer made his league debut for Liverpool on the opening day of the first post-war season (1946-47), although he had actually played in an FA Cup tie against Bolton Wanderers the previous January, when regional leagues were still in operation. Although many of his early appearances for the club came in the half-back line, he was better known as a left-back. Only 22 years old when the Second World War ended, it took a while for him to become a regular first-team player at Anfield and he had to wait until the 1949-50 season for his big breakthrough, a year when he missed just five league fixtures and was also part of the team that contested the club's first Wembley cup final.
Eddie suffered a dreadful leg fracture which caused him to miss the complete 1951-52 season and after bravely recovering from that he fractured his leg in 19 places in a league match at Old Trafford on December 19, 1953. Suffice to say he never played professional football again and was indeed lucky to walk properly. His employers granted him a testimonial match on September 19, 1955, where a combined Liverpool/Everton team played a Lancashire XI which attracted 41,266 spectators where Spicer pocketed £4,500. Testimony indeed to the high esteem in which he was held by colleagues and supporters alike.