Police said they had received around 200 referrals to the Prevent programme from April to the end of July – around twice the number of referrals recorded in the previous four months.
The figures were released by Simon Cole, the National Police Chief Council’s lead spokesman on de-radicalisation efforts.
“Even though these referrals from the public are increasing, we still need more people to have the confidence to tell our safeguarding experts if they are worried about someone’s behaviour,” Mr Cole said.
Prevent is a voluntary programme aiming to intervene early to stop people being drawn into violent extremism.
The scheme has been credited with helping disrupting more than 150 attempted trips to conflicts in Iraq and Syria.
About 55 to 60% of referrals were related to possible involvement by British individuals with Islamic State militants, Mr Cole said.
But the programme is highly controversial because many Muslims believe it has been used as a tool to spy on their communities rather than simply sway potential militants from becoming radicalised.
Critics have called it “toxic”, urging the Government to scrap it or at least review it.
Mr Cole said the number of referrals made to Prevent by members of the public was still relatively low, with 500 made in 2016 and 2017 compared to an annual total of about 6,300. The other referrals were made by Government or police bodies or other public organizations.
About 15% of the referrals were related to right-wing extremism.
Officials said the number of referrals about suspected right-wing extremists had doubled since the murder in June 2016 of Jo Cox, the MP who was killed by a loner obsessed with Nazis and white supremacist ideology.
Mr Cole urged everyone involved in the scheme to “challenge damaging myths and be more transparent in our approach”.
“We would rather people show concern before something happens,” he said.
Referrals are assessed by a number of agencies and not all are ultimately deemed to require intervention.
Britain is on its second highest threat level – “severe”, meaning another attack is highly likely.
In the past few months it has been hit by four deadly attacks.
In March, a man killed five people after driving into pedestrians on Westminster Bridge in London before stabbing a policeman to death outside the Houses of Parliament.
That was followed by a suicide bombing at an Arian Grande pop concert in Manchester which left 22 dead, many of them young.
In April eight people died after three Islamist militants drove into pedestrians on London Bridge and stabbed people at nearby restaurants and bars.
Two weeks later a van was driven into worshippers near a London mosque which left one man dead.