The club was established in 1928 as Woolwich Borough Council Athletic Club. They joined the Woolwich and District League and were champions in their first season. The following season saw them join Division One of the Western Section of the
Kent County Amateur League. In 1934 Division One was renamed the Premier Division, and after finishing second-from-bottom of the division in 1934–35, the club were relegated to Division One. They finished bottom of Division One in 1939–40, but the league was largely abandoned the following season due to
World War II. Woolwich Borough Council rejoined the Kent County Amateur League in 1947, and despite their pre-war position, the club were placed in the Premier Division of the Western Section. They won the Senior Division in 1979–80, earning promotion to the Premier Division. In 1982–83 the club won the league's Senior Cup. In 1984 they transferred to the
Kent League. They won the League Cup in their first season in the league, before going on to win back-to-back league titles in 1986–87 and 1987–88, as well as winning the League Cup for a second time in 1986–87. In
2016–17 the club finished third in the division, qualifying for the promotion playoffs. However, they lost 4–3 to
Corinthian-Casuals in the semi-finals. Although a fourth-place finish the
following season saw the club finish fifth and reach the play-offs again, they lost 3–0 to
Corinthian-Casuals in the semi-finals. At the end of the season they were moved into the South East Division as the league was reorganised. In
2018–19 Greenwich finished bottom of the South East Division and were relegated to the Premier Division of the Southern Counties East League (the renamed Kent League). They resigned from the league in January 2020. ==Ground==