British prime minister David Cameron says he will introduce inspections for Islamic schools and will shut down those that teach hate.

In a speech to the Conservative Party annual conference in Manchester, Mr Cameron vowed to keep Britain safe by targeting Islamic State terrorists in Syria and cracking down on religious schools that radicalise students.

"Be in no doubt: if you are teaching intolerance, we will shut you down," he warned schools.

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Key points: Cameron targets schools teaching hate

Cameron targets schools teaching hate He uses speech to calm Eurosceptics

He uses speech to calm Eurosceptics Vows to tackle poverty, inequality

"Boys who could do anything they wanted to in Britain, who benefitted from everything this country had to offer instead ending up in the desert wielding a knife."

There are about 2,000 madrassas in England and Mr Cameron said the majority will have no problem opening their doors to inspectors.

Much of the focus on the sidelines of the conference was on who had auditioned best to replace Mr Cameron.

Mr Cameron himself gave few clues as to his preferred candidate, instead aiming his guns on Labour's new leftist leader Jeremy Corbyn.

"Thousands of words have been written about the new Labour leader," he told the audience.

"But you only really need to know one thing: he thinks the death of Osama bin Laden was a 'tragedy'.

"We cannot let that man inflict his security-threatening, terrorist-sympathising, Britain-hating ideology on this country we love."

Analysis by Europe correspondent Lisa Millar British prime minister David Cameron has five years left to govern and he used this moment to deliver a message not only to his own party, but his opponents in Labour and the cast of possible successors lining up to take his place. "As you know, I am not going to fight another election as your leader. So I don't have the luxury of unlimited time. Let me tell you: I am in just as much of a hurry as five years ago," Mr Cameron said. He struck a liberal tone on racism, showed a more compassionate and inclusive side to the party with a clear social mission, talked of massive national infrastructure projects, and railed against the gender pay gap and racism. This is not a leader moving to the centre ground. He is almost shifting to the left of it. "The British people are decent, sensible, reasonable and they just want a government that supports the vulnerable, backs those who do the right thing and helps them get on in life," he said. At the halfway mark of his leadership of the country, Mr Cameron wants this to be the turnaround decade. He has vowed to tackle deeper social problems including the housing shortage crisis that has forced a new generation out of the market. For the last four days he has sat and listened to the speeches of those who are tipped as his successors — chancellor George Osborne, London mayor and now MP Boris Johnson and home secretary Theresa May. It was if they were auditioning for the job, but Mr Cameron was making it clear he is not going anywhere. The next election will be held in 2020 and there will be a new leader taking the Tories into the campaign. What Mr Cameron does between now and then will determine how successful they will be.

Mr Cameron used much of his speech to calm Eurosceptic members of his party, saying he would make sure Britain never signed up to the EU's stated goal of "ever closer union".

But Mr Cameron also said Britain had influenced Europe before and could remain strong in Europe, promising he could get a "better deal and the best of both worlds".

"We don't duck fights. We get stuck in. We fix problems," he said.

"We all know what's wrong with the EU — it's got too big, too bossy, too interfering.

"But we also know what's right about it — it's the biggest single market in the world.

"Believe me, I have no romantic attachment to the European Union and its institutions.

"I'm only interested in two things: Britain's prosperity and Britain's influence.

"That's why I'm going to fight so hard in this renegotiation."

Mr Cameron has conceded ground to his vocal Eurosceptics by offering a referendum on Britain's membership of the European Union by the end of 2017, hoping to bury an issue that has divided the party for years and helped bring down two former prime ministers.

'A greater Britain' targets poverty and inequality

He personally favours Britain staying in a reformed EU, but would "not be heartbroken" to leave.

"A greater Britain is one that is strong in the world — and that should mean one that is strong in Europe, too," he said.

His call for a "greater Britain" also envisaged a country tackling some of its most entrenched problems such as poverty and inequality.

Mr Cameron, who at 48 has said he will step down by 2020 after his second term as prime minister, said Britain had to offer more opportunities to minorities and tackle segregation to inspire young people.

He called on the Conservative Party to become the party of the working people and claim the "centre ground" as the main opposition Labour Party turns further left.

To attract younger voters — many of whom have backed Labour's new far-left leader Mr Corbyn, he unveiled a new policy to spur home ownership, striking at criticism that his Conservative government is failing growing numbers of Britons unable to buy a house.

"When a generation of hardworking men and women in their 20s and 30s are waking up each morning in their childhood bedrooms — that should be a wakeup call for us," Mr Cameron said.

Home ownership has long been a totemic issue for the Conservative Party and strikes at the new leader of the Labour Party, who had promised to do more to help people afford homes.

"So I believe that we can make this era — these 2010s — a defining decade for our country, the turnaround decade," he said.

"We can be that greater Britain."