Mrs Evelyne Hinde was the first head Teacher of Cleeve Park School and oversaw its formation.

The building has been extended and developed several times over the years most notably with a new wing added in 1990 and then a further section in 1995, both opened by the then MP for Bexley Sir Edward Heath.

In Summer of 2015, a maths and PE teacher "Mr Thompson" received a Golden Apple award from Good Morning Britain, and a film crew came into the school to record this event.

The school took delivery of 6 Portacabins in late October/Early November 2023 to make up for the loss of teaching space.

In February 2024, the school was inspected by Ofsted and received a "Good" rating across all areas,[5] showing a significant development since the previous "Requires Improvement" grade given in 2019.