Eight people a day were referred to the government's deradicalisation scheme Channel this summer. National Police Chiefs' Council Figures show 796 referrals between June and August.
More than a third of those referred to the programme over the period were under 18. There were more referrals during the period than during the whole of the 2012-2013 period when the scheme was rolled out, and more than double the number of referrals than in the first three months of the 2014-2015 period.
The increase comes after the government placed legal responsibility on public bodies including schools, prisons and local councils to refer those thought to be at risk of being drawn into terrorism. Both those at risk of being drawn into far-right and Islamic terrorism are referred to the programme.
Haras Rafiq, of the counter-extremism Quilliam Foundation, said that the rise in figures comes after "the lure of extremism has increased over the last year both from an Islamist and far-right perspective".
He added: "There is a symbiotic relationship between the two. More effort needs to come from civil society so that we build resilience in our communities so that these numbers come down."
Last week a teenager from Blackburn, Lancashire, was found to have been encouraging terrorist attacks in Australia on Anzac Day despite being enrolled on the programme.