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The Rockets were formed in 1997 by current owner Gary Johnson together with his son Matt, starting in Division 3. The club won promotion at the first attempt, and in the National Basketball League reorganisation of 2000, England Basketball replaced Division 1 with the eight-team NBL Conference as the second-tier. Subsequently, Division 2 became Division 1 where the Rockets found themselves.

The Rockets remained in Division 1 for just one season, finishing second and beating Oxford in the Championship Final, thus winning promotion to the NBL Conference. In the 2001-02 season they finished seventh in the NBL Conference. In the following season, the Rockets continued their rise, finishing in third place. In 2003, the National Basketball League was rebranded as the English Basketball League, and once again was restructured with a new format, with Rockets finishing in second place in the new EBL Division 1. In the following season the Rockets finished third and were runners-up to Worthing Thunder in both the 2005-06 and 2006-07 seasons.

The club completed its most successful season ever in 2008-09, going undefeated to win all four national championships. The club applied to join the British Basketball League (Top division of the British Basketball System) as a member franchise for the 2012–13 season but was unsuccessful. In the 2013-14 season the Rockets completed the treble and were Play Off Championship finalists. Rockets’ Ladies won the Division 2 Southern league in 2014. As a stepping stone into the Senior Men's team, the Rockets’ run academies at the John Madejski Academy and the Henley College.

The club has squads ranging from developing Under-12s to the Division 1 senior men's side, and coaching staff regularly visit local schools and run satellite clubs as part of the Community Rockets scheme.

In 2022, the Rockets applied to join the British Basketball League starting from the 2023–24 season.