Media playback is unsupported on your device Media caption Theresa May: "We need to see if there are additional steps we should be taking to prevent radicalisation"

Thousands of people are potentially at risk of being radicalised in the UK, Home Secretary Theresa May has said.

She also told BBC One's Andrew Marr Show that those at risk were at "different points on what could be a path to violent extremism".

Mrs May said a new taskforce would look at whether new powers were needed to tackle radicalisation.

Three more arrests have been made in connection with the killing of soldier Lee Rigby in Woolwich.

On Sunday, the family of Drummer Rigby visited the scene of his death and Woolwich Barracks.

Two men already arrested on suspicion of his murder remain in custody in hospital in a stable condition.

Michael Adebolajo, 28, and Michael Adebowale, 22, were shot and wounded by police at the scene in Woolwich on Wednesday after the killing.

The Metropolitan Police said counter terrorism officers arrested three men, aged 21, 24 and 28, in London on Saturday evening on suspicion of conspiracy to commit murder - a Taser was used on two of them.

Media playback is unsupported on your device Media caption Former Home Secretary Alan Johnson: "The first role of government is to protect its people"

'Resignation issue'

Mrs May said "500 officers and others" were working on the case, including counter terrorism officers brought in from elsewhere in the country.

She said the government had introduced "a new programme, which is not for those immediately at danger of radicalisation, but for those who are perhaps further out". Around 2,000 people had been worked with within the last year, she added.

When asked if she would now push ahead with a Communications Data Bill, Mrs May said: "The law enforcement agencies, the intelligence agencies, need access to communications data and that is essential to them doing their job."

Mrs May has previously said such a bill would help modernise crime-fighting laws, to combat criminals' use of internet-based phone calls and social media sites.

Analysis The killing of Drummer Lee Rigby has posed a series of questions for the government to grapple with. The central one is this: what more, if anything, can ministers do to reduce the likelihood of other similar attacks? The Home Secretary Theresa May is very keen on giving the police and intelligence agencies more power to access details of online communications where necessary. There is no such thing as a trade union of former home secretaries. But on this issue, it sounds as though there is. Labour's Lord Reid and Alan Johnson and the Conservative Lord Howard all agree with her. In short, their argument is we have seen the classified files and the spooks need this power. Critics - including most Liberal Democrats - accuse them of going native and backing a "snooper's charter". The other big question is whether the government's existing policies for dealing with extremism and radicalisation are up to the job. A so-called "taskforce" will look into this. Money is not everything in devising government policies that work. But critics will point to, and ministers will have to defend, the big cut in the annual budget for the Prevent strategy two years ago.

The bill was sent back for reassessment in December after criticism from a joint committee of MPs and peers, includes plans for internet service providers having to store for a year all details of online communication in the UK.

Mrs May said the government needed to look at how organisations outside government could help, such as Ofcom.

Senior Whitehall sources have previously confirmed to the BBC both suspects arrested at the scene of the killing of Drummer Rigby were previously known to security services.

When asked if there were mistakes made by the security services in dealing with this case, Mrs May said: "What we have is the right procedures which say when things like this happen we do need to look at whether there are any lessons to be learned."

She also said the government's Intelligence and Security Committee would review the security service's actions in this case, but added that this report "won't happen immediately, because they will look back at the operation and the case".

Former Home Secretary Alan Johnson also told the programme a Communications Data Bill should be "on the statute book before the next election".

"It is a resignation issue for our home secretary if the Cabinet do not support her in this central part of what the security services do," he added.

Lord Carlile, the Lib Dem former independent reviewer of terror laws, told the BBC that while it was not known whether the bill would have prevented this incident, "it might have [and] it would certainly help to prevent similar incidents in the future".

Image caption Michael Adebowale was photographed brandishing a knife and speaking to a woman at the scene

But Lib Dem deputy leader Simon Hughes said there is "no evidence at all" that the bill could have prevented the killing.

In other developments:

Prayers were said on Sunday at a service dedicated to Drummer Rigby at St Peter the Apostle Roman Catholic Church, in Woolwich, at a service at the town's St Mary Magdalene Parish Church and in his local church in his home town of Middleton, Greater Manchester

A 29-year-old man, arrested on Thursday on suspicion of conspiracy to murder, has been bailed to return pending further inquiries

French authorities are investigating whether the stabbing of a soldier in a Paris suburb was a copycat attack. The soldier, who was stabbed in the neck by an unknown man who escaped, is in a stable condition

MI5 director general Andrew Parker is expected to present an initial report to a Parliamentary committee next week about what the security services knew about the two murder suspects

There has been a large increase in anti-Muslim incidents since Wednesday's murder, an inter-faith charity has said

Mrs May said the government taskforce announced this weekend would "be able to look across the whole of government" and look at institutions such as universities and prisons to see if more could be done in tackling the issue of countering extremism.

The special government committee being set up will be chaired by the prime minister and will include senior cabinet ministers and security chiefs.

Image caption People paid their respects to Drummer Rigby in Middleton, his home town

Downing Street sources have said the new taskforce will "build on" Labour's Prevent Strategy, which was set up to counter radicalisation.

The coalition reviewed this Prevent Strategy in 2011 reducing its annual budget from £63m to £36m saying at the time that some of the money was going to groups who should have been confronted.

Hazel Blears MP told the Observer that vulnerable people who are likely to be influenced by extremist preachers were being spotted too late.

Meanwhile the Independent on Sunday is one of a number of papers to feature a picture it says is of Mr Adebolajo appearing in court in Kenya in 2010 accused "of being at the centre of an al-Qaeda-inspired plot".