Dagenham & Redbridge have only existed in their current form since 1992 when Dagenham FC, who played at Victoria Road, D&R's current ground, merged with Redbridge Forest FC.
Dagenham FC were formed in 1949 and played in a number of leagues, including the Athenian League, before joining the Isthmian League in 1973. They reached the final of the FA Amateur Cup in 1970 and 1971, losing to Enfield (5-1) and Skelmersdale United (4-1) respectively. They were FA Trophy finalists in 1977, losing 2-1 to Scarborough and then went on to win the FA Trophy in 1980, beating Mossley 2-1. 
Dagenham joined the Alliance Premier League in 1982 but were relegated back to the Isthmian League in 1988 where they remained until their merger with Redbridge Forest in 1992.
Redbridge Forest came out of a complicated evolution involving three clubs; Ilford, Leytonstone and Walthamstow Avenue. 
Ilford were formed in 1881 and were FA Amateur Cup finalists in the last ever time the cup was held in 1974, losing 4-1 to Bishops Stortford. They won the trophy in 1929 and 1930. They were also Isthmian League champions in 1907, 1921 and 1922. In 1979 their ground, Lynn Road, was sold and they merged with
Leytonstone FC. 
What is left of Lynn Road, Ilford's old ground. 
Leytonstone FC began life in 1886 as Cedars FC and were renamed in 1892 as Leytonstone FC. Their ground was near Leytonstone High Road They were Isthmian League champions in 1938, 1939, 1947, 1948, 1950, 1951, 1952 and 1966 and were FA Amateur Cup winners in 1947, 1948 and 1968. They beat the Bees in the 1948 final, 1-0. In 1979 they merged with Ilford FC to form Leytonstone & Ilford. 
Walthamstow Avenue were formed in1990 were formed in 1900 and originally all the players were meant to live in the avenues of Walthamstow, hence the name. They played at Green Pond Road stadium. They won the Isthmian League in 1946, 1953 and 1954. One of their players, Jim Lewis won a full England international cap in 1939. They won the FA Amateur Cup in 1952 and 1961. The 1952 final was the first Amateur Cup final to attract a 100,000 gate at Wembley. In 1988, the club merged with Leytonstone & Ilford. 
Leytonstone & Ilford won the Isthmian League in 1982 and in 1983 the name changed slightly to Leytonstone/Ilford. In 1988, then came the further merger with Walthamstow Avenue, though the name remained the same and they won the Isthmian League again in 1989 but they were denied promotion to the Conference because of ground problems. 
Shortly after the club was renamed Redbridge Forest to take into account the merger of Walthamstow Avenue and they won the Isthmian League again in 1991, but then had to move to ground share with Dagenham FC to enable them to be promoted to the Conference as Dagenham had a Conference graded ground. In their only Conference season, Redbridge finished a respectable 7th. However, in 1992 they merged with Dagenham FC to become Dagenham & Redbridge FC.
Dagenham & Redbridge were FA Trophy finalists in 1997, losing to Woking, 1-0. In 2000, they won the Ryman League and were promoted to the Nationwide Conference. In 2002, they finished as runners up to Boston United. However, at that time only the champions were promoted to the football league; there were no play-offs. In 2007, they won the Conference and were promoted to League Two.
Grateful thanks to DiggerDagger.com for their fantastic website. You can visit their site at www.fansfocus.net/dagenhamandredbridgeWell worth a visit, I think.