Home Secretary Theresa May has launched the government's updated strategy for tackling terrorism by saying there needs to be better focus on preventing extremism at community levels.
She said a review identified serious failings with the existing policy - known as Prevent - set up in 2007.
Some of the £63m annual budget had reached the extremist organisations it should have been confronting, she said.
Meanwhile, a replacement for control orders has come closer to becoming law.
Speaking in the House of Commons, Mrs May said the strategy had failed to tackle the extremist ideology which "inspires would-be terrorists to seek to bring death and destruction to our towns and cities".
"In trying to reach out to those at risk of radicalisation, funding sometimes even reached the very extremist organisations that Prevent should have been confronting.
"We will not make the same mistakes," she said.
In her foreword to the review, Mrs May said the monitoring and evaluation of Prevent projects "had not been robust enough to justify the sums of public money spent on them".
The revised strategy will see £36m spent and 25 areas in England targeted as priorities.
They include Birmingham, Leicester, Luton, Manchester, Leeds and some London boroughs.
It will also withdraw support from extremist groups - even non-violent ones - and cut off funding to those opposed to what the government calls "fundamental and universal" British values.
Mrs May said the strategy would be targeted against "those forms of terrorism which pose the greatest risk to our national security, currently al-Qaeda and those they inspire".
"But Prevent must also recognise and tackle the insidious impact of non-violent extremism, which can create an atmosphere conducive to terrorism and can popularise views which terrorists exploit," she said.
Critics of the government's new policy argue there are some hardline conservative groups who have theological arguments to defeat al-Qaeda recruiters on Britain's streets.
These groups now face being marginalised from government funding.
But Lord Carlile of Berriew, the independent reviewer of Prevent, said: "Many Muslims and Muslim groups have stepped up to the plate and are able to do the work with government and local authorities to deal with radicalisation.
"Government does not need to have truck with extremists, and it won't."
The new strategy also puts a renewed focus on the use of the internet and says the government will consider a "national blocking list" of violent and unlawful websites.
Under the plans, computers in schools, libraries and colleges will also be barred from accessing unlawful material on the internet.
But Ms Cooper said there was a gap between Mrs May's rhetoric and the reality of the government's policy on terrorism, while budget cuts would make it more difficult for Whitehall to deal with extremists.
"We support updating the Prevent strategy but there is a massive gap between your rhetoric today and the reality of your policies.
"Where you should be building consensus around counter-terrorism, instead you have been political point-scoring and you have set out no actual proposals as to how you would deliver in such an important area," she said.
Ms Cooper also attacked the government for failing to ban one radical Islamist group, Hizb ut-Tahrir, even though it pledged to do so while in opposition. Labour ministers said they would ban it, but did not.
Mrs May said the government was keeping the group "under constant review".
Maajid Nawaz, executive director of counter-terrorism think-tank Quilliam, said the new strategy was a step in the right direction.
But he warned that its definition of Islamism was "so broad that it fails to distinguish between Islamists and politically active Muslims inspired by Islam".
"This unnecessarily smears ordinary politically-active Muslims and works to the favour of Islamists who benefit from hiding behind such blurred distinctions," he said.
But Chief Constable Sir Norman Bettison, the lead on the Prevent strategy for the Association of Chief Police Officers (Acpo), said Acpo had been "fully supportive of this government review".
"The effects of Prevent policing have not caused widespread damage or harm to relationships between Muslim communities and the police.
"Instead communities are increasingly taking the lead in challenging violent extremism," he said.
Prevent was originally launched after the 7 July bombings in 2005 to stop the growth of home-grown terrorism.
Previously, Mrs May has said that, as a result of the strategy's review of government support, about 20 of the organisations that received funding over the past three years would have their cash withdrawn.
On Tuesday night, new measures to replace controversial control orders moved a step closer to becoming law after the bill gained an unopposed second reading.
Under the new regime - known as T-Pims (Terrorism Prevention and Investigation Measures) - terror suspects who cannot be prosecuted or deported will still face significant restrictions on their liberties.
Control orders place terrorism suspects under close supervision, and critics have said the new system is little more than "control orders lite".
Mrs May told the Commons that T-Pims would be "more focused and targeted" than the control orders regime set up under Labour, which was "neither perfect nor entirely effective".