Tougher conditions could be imposed on people seeking asylum or leave to remain in the UK as part of moves against those inciting terrorism.
Police are now searching a house in Aylesbury
Home Secretary Charles Clarke has ordered an immediate review of his powers to exclude and deport people.
The moves come as Downing Street said talks aimed at getting consensus on new terror laws in the wake of the London bombs would begin on Monday.
Opposition MPs say they want agreement but warn against "knee-jerk reactions".
Mr Clarke on Thursday briefed the Cabinet about the review of his exclusion and deportation powers.
He wants to ensure that any non-British citizen suspected of inciting terrorism is deported immediately.
There would be agreements with North African countries to make sure asylum seekers were not tortured on return to their country of origin, says No 10.
The home secretary also wants to ensure he automatically reviews cases where people banned from other countries try to come to the UK.
It follows worries about some radical preachers coming to the UK.
In 2004, 14 people were banned from coming to the UK under existing powers, 12 of them on national security grounds.
Drive for agreement
Efforts to examine what new anti-terror measures are needed after the bombings, which killed 52 people, are being stepped up.
Downing Street says it wants to build consensus about the content of new laws and the pace at which they are introduced.
Mr Clarke will meet his opposition counterparts - Conservative David Davis and Lib Dem Mark Oaten - next Monday.
On Tuesday, Tony Blair will meet Muslim community leaders, as well as Conservative leader Michael Howard and Liberal Democrat leader Charles Kennedy.
The prime minister will then host a meeting of senior members of the intelligence agencies and police on Thursday. He will meet Mr Howard and Mr Kennedy again the following Monday.
Mr Blair's official spokesman said: "We stand ready to give the police and the security services any powers they need as a result of this atrocity and the investigation into it."
'Do not rush'
Earlier, Mr Howard said he hoped there could be "genuine consensus" over new measures.
"We are all in this together," he said. "We all have to work together as a national community - Christian and Muslim, Hindu and Jew - to deal with this danger."
Mr Oaten said the Lib Dems, like the Tories, had already called for a new offence of making "acts preparatory to terrorism" and would look at the idea of outlawing incitement to terrorism.
The Lib Dem spokesman said the starting point was to try to agree consensus.
But he warned: "If we feel that we're having knee-jerk rushed legislation then despite what took place last week we have a responsibility to make sure we have good robust laws which work in this country."
One of the bombers reportedly visited an Islamic study camp in Pakistan earlier this year.
Foreign Secretary Jack Straw told reporters Pakistan faced a big challenge to improve such religious seminaries - known as Madrassas.
"We are concerned about what goes on in some, though not all, of the Madrassas in Pakistan but so too is President Musharraf and many, many people in the Pakistan political parties and Pakistan Government," he said.
Mr Straw said there was "intensive and increasingly substantial co-operation" with Pakistan on counter-terrorism but he refused to discuss contacts on the current investigation.