Tony Blair has outlined a raft of plans to extend powers to deport or exclude foreigners who encourage terrorism.
The UK can already exclude or deport those who pose a threat to security and Mr Blair said he also wanted to clamp down on those who advocated terror.
The prime minister said he was prepared to amend human rights laws to make deportations more straightforward.
But Lib Dem leader Charles Kennedy said Mr Blair's announcements would put the cross-party consensus under strain.
The measures came as Scotland Yard confirmed they had arrested two more people in London earlier this week in connection with the 21 July attempted bombings.
It brings the total of people still in custody over the bomb attempts to 17 - three of whom have been charged.
On the new anti-terror package, Mr Kennedy warned that plans to ban Muslim organisations, powers to close mosques and deport people who "visit particular bookshops and websites" risked "inflaming tensions and alienating people".
Shami Chakrabarti, director of civil rights group Liberty, said Mr Blair has attacked key human rights and would jeopardise national unity.
Home secretary to consider deporting any foreigner involved in listed extremist centres and websites
Make justifying or glorifying terrorism anywhere an offence
Automatically refuse asylum to anyone with anything to do with terrorism
Examine calls for police to be able to hold terror suspects for longer before pressing charges
Use more control orders against British terror suspects
Create a list of preachers who will be kept out of the UK
Conservative shadow home secretary David Davis welcomed the broad thrust of the proposals on exclusions and deportations but he said the consultation period was very short.
Mr Davis said: "It is vital that the home secretary is able to use his powers to deport or exclude non-UK citizens who threaten our national security - we have been calling for him to use these for some time."
London has been nicknamed "Londonistan" - centre for militant Islam - by some critics who believe the UK has been too liberal towards radical clerics.
At the final news conference before his summer break, Mr Blair said British hospitality had been abused and people should know the "rules of the game are changing".
"People now understand that when we warned of the terrorist threat it wasn't scaremongering it was real, he said.
Among the planned changes, Mr Blair said people would be refused asylum if they had been involved in terrorism.
A one-month consultation would be held on the new grounds for excluding and deporting people - something which does not require new legislation.
Mr Blair said Parliament might be brought back from the summer recess early to discuss other measures.
These will include measures to tackle those advocating violence to further a person's belief, justifying or validating such violence, or fostering hatred.
The Hizb ut Tahrir organisation and Al-Muhajiroun - or its successor group - are to be banned, Mr Blair announced.
"We will also examine the grounds for proscription to widen them and put forward proposals in the new legislation," he said.
Imran Waheed of Hizb ut Tahrir said his group would fight any ban and insisted they were "non-violent".
The Muslim Council of Britain said the ban would be "counter productive".
Mr Blair said British people were tolerant but "there is also a determination that this very tolerance and determination should not be abused by a small fanatical minority and anger that it has".
On Thursday al-Qaeda's number two threatened new attacks on London and blamed the prime minister for the 7 July bombings, which killed 56.
Mr Blair said the British people knew how to deal with such comments, which had been made by those supporting the killing of innocent people in Iraq, Afghanistan and elsewhere.
Metropolitan Police chief Sir Ian Blair argued it would have been better to bring in the new measures at an earlier date but said he was glad action was being taken now.