Eight people a day were referred to the government's deradicalisation scheme known as "Channel" this summer.
Between June and August, 796 people in England and Wales were reported to the programme for possible intervention.
National Police Chiefs' Council figures show more than a third of the total, 312, were aged under 18.
People identified as at risk of being drawn into terrorism are assessed and about a fifth of these are required to attend deradicalisation sessions.
Public bodies such as schools and local councils are legally required to spot such cases.
'Fundamental British values'
The people who end up on the Channel programme have been identified as potentially on a path to violent extremism.
Referrals are most likely to be made in the first instance by those working in public services dealing with vulnerable individuals, such as the education, prison and health sectors.
There were 327 referrals in June, 349 in July, and 120 in August.
There were more referrals over this period than for the whole of 2012-13 - the first year the scheme was rolled out across England and Wales.
It is more than double the level of referrals recorded in the first three months of 2014-15.
By BBC home affairs correspondent Daniel Sandford
The Channel programme is designed to spot people at risk of being drawn into terrorism of all kinds.
People who are identified are then assessed, and in the past around a fifth of them have been required to attend intensive deradicalisation sessions.
This summer's statistic for England and Wales - 327 referrals in June and 349 in July - show the degree of concern among teachers and social workers about the prevalence of extremism.
More than 10 people a day were being referred, and even when the quieter month of August is included the average across the summer was eight a day.
Last week the Channel programme was criticised when a teenager from Blackburn - who was on the programme - was nonetheless found to be threatening his teachers and encouraging a terrorist attack at an Anzac Day parade in Australia.
The government has defined extremism as: "Vocal or active opposition to fundamental British values, including democracy, the rule of law, individual liberty and mutual respect and tolerance of different faiths and beliefs."
The government says the programme is "about ensuring that vulnerable children and adults of any faith, ethnicity or background receive support before their vulnerabilities are exploited by those that would want them to embrace terrorism".
Haras Rafiq, managing director at security think tank Quilliam, said the figures came after "the lure of extremism has increased over the last year both from an Islamist and far-right perspective".
"There is a symbiotic relationship between the two," he added.
"More effort needs to come from civil society so that we build resilience in our communities so that these numbers come down."
Security Minister John Hayes said: "As a country, we have a duty to challenge, at every turn, the twisted narrative that has corrupted some of our vulnerable young people.
"Referrals to Channel have increased, but only a small percentage of these go on to require specialist intervention support.
"We have dedicated sufficient resources to the programme to cope with demand and we will keep this position under close review."