REME's record in the Quadrangular Tournament is an impressive one. They have won the trophy 16 times since 1969 dominating the early years with an unprecedented run of six titles in a row. This run owed much to the dominant SEME side who swept all before them in Army Inter-unit football. The Corps had to wait until the mid 1990's before it next sustained a run of three titles.
Despite the successes REME have had in the Quads the Massey Trophy has proved to be an elusive prize for REME winning the trophy only once in its inaugural season.
REME matches with the Royal Signals date back to the 1948/49 season. It started its rivalry with the Royal Engineers the following season and Royal Artillery in 1968/69.
Over the years REME have produced some great players who represneted both Army and Combined Services level. Some even went onto make a living in the professional game, most noteworthy in modern times is Guy Whittingham who played for Aston Villa and Portsmouth and Maik Taylor who has played for Northern Ireland at international level and Birmingham City and Fulham in the Premier League.