The government has already started to withdraw state cash from what it regards as suspect Islamist groups that had previously been funded to reach young Muslims at risk of being drawn to terrorist networks. New, tougher criteria are being applied, with hundreds of thousands of pounds being withdrawn from specific groups after it was deemed they were too soft on Islamic extremism.

Ministers are also awaiting a report in the next fortnight from a Universities UK working group, which has been in preparation for a year, on how to combat Islamic extremism on university campuses.

The working group, including eight vice-chancellors, was established in response to the arrest of Umar Farouk Abdulmutallab in the US for an attempted act of terrorism. Abdulmutallab studied at University College London between 2005 and 2008.

The report is likely to call for greater rigour in the selection of speakers and stronger oversight of religious societies. University vice-chancellors have been accused by thinktanks such as Quilliam, a Muslim counter-extremist group, of being complacent about the radicalisation that is taking place in higher education.

Today, it was being stressed by the government that David Cameron's call for a more "muscular liberalism" to combat home-grown terror, made in a speech in Munich on Saturday, was not simply rhetorical. It would lead to practical changes, including the wholesale review of the Prevent strategy set up by Labour.

One outcome is likely to lead to a greater focus on specific areas where propagandists for terrorism are known to be operating, including community centres and gyms. There is also expected to be a clearer separation of resources to fight terrorism, and general community cohesion work.

With Labour claiming Cameron's speech was ill-timed, coming on the day of a march by the English Defence League (EDL), Cameron's aides said he had been preparing the speech since Christmas following seminars at Chequers, and it was always intended to be delivered at the Munich security conference this weekend.

One government source said: "There is going to be a real shift in who we fund and who ministers share platforms with. It has already started. There used to be a view in the home office that the best way to engage dangerous people was through some people who were not themselves extremists, but shared much of their thinking . We think it is better to confront all forms of extremism – the kind of people that support Jihad abroad, but say no Jihad here, or at least not now."

The "British values" set out by Cameron in his speech – freedom of speech, freedom of speech and equality between sexes – will be the criteria by which the government will engage in future.

Haras Rafiq, director of anti-extremist organisation Centri, said he fully supported the prime minister's call for a ban on the public funding of Muslim groups that did little to tackle extremism. He blamed some of the current misdirection of funds on failings by the Prevent programme, which has spent £53m on more than 1,000 counter-terrorism projects since it was set up in 2007 in the wake of the 7/7 London bombings.

Rafiq said: "A lot of funding is going to groups that hold vile views that are not acceptable in a tolerant, liberal society like the UK. Some support suicide bombing, attacks on British troops in Iraq or Afghanistan and other forms of violent extremism, but they are supported by the government so long as they don't support violence in the UK – even where they support unacceptable domestic policies like saying it's wrong for Muslims to vote or it's sinful for a woman to get into a taxi alone with a man she's not related to. But my biggest concern is that by funding and promoting fringe elements within British Muslim society, it is tarnishing the whole Muslim community."

But Mohammed Shafiq of the Ramadhan Foundation, a Muslim youth group, said Cameron had been "deeply irresponsible" to suggest that some publicly-funded groups did little to tackle extremism.

"Where are these Muslim organisations that support extremism? I don't believe they exist, and if the prime minister believes otherwise he should have the confidence to name them." Farooq Murad, secretary general of the Muslim Council of Britain, said it was important to identify which groups Cameron had been referring to. "The MCB itself, though not in receipt of government funding, has consistently spoken in favour of British values that acknowledge universal human rights and pluralism," said Murad.

No shadow ministers today followed shadow justice secretary, Sadiq Khan, in claiming David Cameron was involved in "writing propaganda for the EDL" on the day 3,000 English Defence League members held a rally in Luton. Yvette Cooper said Cameron was "unwise" not to have also criticised the EDL, but foreign secretary William Hague said a PM's speech should not be shelved "because some people have chosen to march down a street".

Trevor Phillips, Equalities and Human Rights Commission chair, refused to criticise the claim that multiculturalism had failed, but said the PM "may have made life a bit more difficult for himself" by combining the issues of terrorism and integration in one speech.