The coalition's strategy to counter Islamist extremism is failing, according to an outspoken intervention by the former cabinet minister who ran the programme under the last government.

Speaking following the Woolwich attack, Hazel Blears MP, who as communities secretary led the Prevent strategy under Labour, told the Observer that people vulnerable to the messages of extremist preachers were being spotted too late. She said it had been a serious mistake to dismantle Labour's policy of funding local authorities that have a population more than 5% Muslim, to help them curb radicalism by engaging and funding community groups, Islamic societies and mosques.

The mother of Michael Adebolajo, one of the two men arrested over the murder on Wednesday of Lee Rigby, a soldier in the 2nd Battalion the Royal Regiment of Fusiliers, is said to have sought help at a mosque over her son's vulnerability in his teenage years, but the system did not respond. Blears, who is a member of the cross-party committee of MPs that monitors the intelligence services, said she was very worried that Prevent was now "basically dealing with people who are already crossing that line" into radicalism, rather than making an early identification of those who were vulnerable to extremist Islamic preaching. Her comments come in another eventful day following the attack.

Greenwich university confirmed that Adebolajo had studied there in 2003/2004 and 2004/2005, but said that he had been asked to leave due to his poor academic performance. The university said that the second suspect, Michael Adebowale, 22, had not attended the institution. The university announced that it was opening an investigation into any evidence of extremism on campus. Last night it emerged Adebowale had been detained by police two months ago after shopkeepers in the area had complained about his preaching activities in the street. He was released without charge.

The BNP was accused of exploiting Wednesday's attack to further its "own poisonous ends" after the far-right group announced it would be demonstrating in south-east London, where the attack took place. A huge rise in the number of anti-Muslim incidents has also been recorded, with 162 calls made to a helpline since the killing – up from a daily average of six. A YouGov poll also shows – amid a generally tolerant attitude towards Islam – an increase in the number of people, particularly from older generations, who believed there would be a "clash of civilisations" between British Muslims and native white Britons. This figure rose from 50% in November 2012 to 59% on Thursday and Friday.

Questions were being asked last night about how much MI5 knew of the two suspects, after Abu Nusaybah, a friend of Adebolajo, claimed that the secret services had tried to recruit the murder suspect in Kenya, where he was allegedly assaulted by local security forces. That claim has at least one precedent in British courts. In 2009, four Britons held in Kenya testified that they were interrogated under threat of torture by the country's anti-terrorism agency while MI5 agents declined to intervene.

Nusaybah was arrested on terrorism charges following an interview with Newsnight on Friday evening. The prime minister has announced that a preliminary report from MI5 on what the organisation knew of the men would be given to the parliamentary watchdog on which Blears sits this week.

The former minister's comments will inevitably lead to a debate about whether the coalition rolled back the Prevent policy too dramatically. The Labour government's policy of encouraging local authorities to fund sympathetic Islamic groups was attacked in its latter years by critics who claimed that the government was establishing a network of spies to monitor Muslim communities. It was also claimed that extremist groups had received funding, and the strategy was redrawn in 2011. Funding was removed from organisations that were said not to support "British values" and Prevent funds were to no longer to be used for "community interventions". Blears said the coalition had been mistaken in disengaging from local authorities and focusing Prevent solely on stopping extremists being drawn towards terrorism. She said that the case against Labour's Prevent strategy had proved largely false, with the Home Office reporting in 2011 that there was no evidence of spying nor anything to "indicate widespread, systematic or deliberate funding of extremist groups", although some with extremist ideology had received funding as part of the engagement strategy.

Blears, MP for Salford and Eccles, said: "I am very worried that over the last couple of years, the communities department, which works very closely with local authorities, has abandoned this territory.

"Now the main thrust is with the police. They do a fantastic job but they are dealing with people who are already crossing that line. Counter-extremism isn't just about tackling the people you already know are radicalised. It is about trying to work with local communities before they get to that point so that good decent people in the community can protect young people from being groomed and getting these ideas in the first place and much of what was done in the Prevent programme was about empowering women, young people.

"The police have their own intelligence on the ground and they have neighbourhood policing. They are out and about in the community but in a way it is one side of the picture. Local authority, school governors, people in community groups will have their information as well. The difficulty is when that information is then portrayed as spying on people."

A Home Office spokesman said: "The police cannot and do not deliver Prevent work on their own. We work very closely with local authorities in our priority areas who engage with a range of partners including faith institutions and civil society groups. We also work with other local authorities as required. Prevent is an integral part of our counter-terrorism strategy and aims to stop people from becoming terrorists or supporting terrorism."