Scotland Yard is checking for possible links between the man who massacred 76 people in Norway and British far-right and anti-Islamic groups.
Prime Minister David Cameron said he took the claims "extremely seriously".
Anders Breivik, 32, who admits a bombing and shootings on Friday, wrote a manifesto in which he said he was recruited by two English extremists.
But police sources say nothing significant has been found to suggest he planned the attacks in the UK.
The UK National Security Council has called on police and security services to re-assess the level of scrutiny of far right groups.
Following a meeting of the council on Monday morning, a Downing Street spokesman said: "We are going to take stock of what happened in Norway and see if there are lessons to be learned."
Speaking at a press conference with the Spanish prime minister, Mr Cameron said: "Everyone in Britain shares in the sorrow and the anger at the despicable killing which took place on Friday.
"Britain and Norway have been good allies and neighbours in very dark days before and we know the resilience and the courage and the decency of our Norwegian friends will overcome this evil."
The Metropolitan Police said the force was liaising with the Norwegians, although no formal police investigation is under way.
Norwegian police are investigating his claims that he has "two more cells" working with him.
In his manifesto, Mr Breivik claimed he was recruited by two English extremists at a meeting in London in April 2002 attended by a total of eight people.
English Defence League
He signed the document with an anglicised version of his name - Andrew Berwick - and it was datelined "London, 2011".
The manifesto said he used to have more than 600 English Defence League (EDL) members as Facebook friends and had had contact with EDL leaders.
The EDL has denied any official contact with him.
A statement on its website said: "We can categorically state that there has never been any official contact between him and the EDL.
"Our Facebook page had 100,000 supporters and receives tens of thousands of comments each day. And there is no evidence that Breivik was ever one of those 100,000 supporters."
EDL leader Stephen Lennon told BBC Two's Newsnight programme he never met Mr Breivik but admitted he knew Daryl Hobson, who had claimed the gunman had met members of the group.
Mr Lennon said he did not believe Mr Breivik had been on an EDL demonstration, adding the Norwegian had described his group as "naive fools".
He condemned the attacks in Norway but warned a similar atrocity could happen in the UK if concerns over Islam continued to be ignored by politicians and the media.
He said: "We stand against extremism and we condemn all acts of violence but at the same time you have to give people in our community that are concerned about the threat of Islam, which is a genuine threat, you have to give them an opportunity to have a voice.
"I share the same fact that Islam is a threat but we completely condemn any acts of violence against innocent people. What has happened over there (Norway) is horrific and will be remembered for the rest of eternity as a disgusting, deranged attack."
The prime minister visited the Norwegian embassy in London on Monday, where, after a brief meeting with deputy head of the mission Arne Bjornstad, he signed a book of condolence.
Mr Cameron wrote: "Everyone in Britain stands with the people of Norway at this time of great sadness and mourning.
"We remember those who lost their lives in Oslo and Utoeya on 22nd July in an act of appalling barbarism.
"We know that the courage, the decency and the resilience of the Norwegian people will overcome this evil."
Flowers and candles have been placed outside the embassy, where its flag has been flying at half-mast.
Foreign Secretary William Hague said a British police officer was co-ordinating the investigations with the Norwegian authorities out of the British embassy.
He said: "It remains the case that the single biggest terrorist threat to this country remains al-Qaeda, or people inspired by al-Qaeda, but what has happened is a reminder that it is not the only source of violent extremist or terrorist attack."
Police sources say any links between Britain and Mr Breivik appear to be historical.
The gunman, a Norwegian with far-right links, said he had planted the bomb in central Oslo and later carried out a massacre at a youth camp on Utoeya. Police have now revised down how many people were killed on the island to 68 - from 86 - but increased the bomb death toll by one to eight.
He said he had carried out the attacks alone, describing his actions as "gruesome but necessary".
Mr Breivik has made his first appearance in court, although the hearing was held behind closed doors following a ruling by the judge.
In his manifesto, Mr Breivik made repeated references to former UK Prime Ministers Gordon Brown and Tony Blair, accusing them of making London a global hub of Islamist terrorism.
The Prince of Wales was criticised for his patronage of the Oxford Centre for Islamic Studies.
Potential UK targets for attacks are mentioned including North Sea oilfields and the BP exploration office at Dyce in Aberdeen.
According to the Daily Telegraph, a Scotland Yard source said he was not thought to have visited the UK this year.
The Labour Leader Ed Miliband said he and people across Britain were shocked by the killings.
"I'm sure all of the people of Britain have huge sympathy with family and friends of those who've have died, and as leader of the Labour party I also want to pay particular condolences because the horrific incident on the island obviously happened at a Labour Youth event."