The 13-year-old twins took their legal challenge to the High Court after being left upset by being stopped and searched at the Climate Camp protest at the power station two years ago.
In a statement, assistant chief constable Andy Adams said: "We have accepted that many people were searched as a result of officer briefings, which took place at the time of Climate Camp. A number of these searches should not have happened."
He added that since the incident the force "has made significant progress" to improve its stop-and-search procedures.
He said that training on the issue was a core subject at Kent Police College and forms part of public order training for all levels of police officer.
During the protest, 100 arrests were made and 46 people were charged, mainly for obstruction and public order offences.
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