Home Secretary Charles Clarke has gained in principle support from opposition parties on the draft legislation which he hopes will become law by December.
The tougher new laws would outlaw indirect incitement of terrorism, including praising those who carry out attacks, as well as making it illegal to receive training in terrorist techniques in Britain or overseas.
This comes as the governments of the United States, Britain and Australia rejected a report saying their involvement in the war in Iraq has raised the risk of terrorist attack.
A report issued by Britain’s respected Royal Institute of International Affairs said the invasion of Iraq has boosted recruitment and fundraising for al-Qaeda, suspected of being behind the bombings.
But British Foreign Secretary Jack Straw said terrorists have struck across the world, “in countries allied with the United States and in countries which had nothing whatever to do with the war in Iraq”.
In Washington, US Defence Secretary Donald Rumsfeld and Australian Prime Minister John Howard said avoiding confrontation does not necessarily make a country safer.
“People who think they can make a separate peace with terrorists will find that it’s like feeding an alligator, hoping it eats you last,” said Mr Rumsfeld.
Meanwhile, more than 500 British Muslim leaders and scholars have condemned the killing of innocent people in the London terrorist attacks, saying suicide bombings are vehemently prohibited.
British Prime Minister Tony Blair will soon meet with Muslim and community leaders to discuss how best to respond to the London bombings, and will seek to find out how young Britons become suicide bombers.
Earlier, Reuters reported that three of the suicide bombers entered Pakistan through Karachi last year, according to immigration officials.
“Shehzad and Sidique visited Karachi in November last year, and went back to London in February,” an immigration official said on condition of anonymity.
He was referring to Shehzad Tanweer, 22, and Mohammad Sidique Khan, 30.
Flight records reveal the two men flew into Karachi on November 19 last year on a Turkish Airlines flight.
Both men left for London from Karachi on February 8.
A Pakistani newspaper has reported that the paid had stayed in Karachi for a week before leaving for Lahore by train.
Tanweer is believed to have visited Faisalabad and Lahore during two trips to Pakistan in recent years, and sources said he visited religious schools in the country in 2004.
Hasib Hussain, 18, entered Karachi from Riyadh, Saudi Arabia, on July 15, 2004.
The British government has not yet confirmed the reports.
“So far we have not found the links of Tanweer and Khan to Hussain, but it could be possible that they were on different assignments,” a Karachi-based intelligence official told AFP.