By Nick Assinder
Political Correspondent, BBC News website
Tony Blair's previous attempts to find a consensus over anti-terror laws collapsed amid bitter recriminations and party divisions. The London bombings have changed that.
Home Secretary Charles Clarke has won support from the opposition parties for new laws to be pushed through parliament by the end of the year.
Political leaders back new laws
Legislation creating offences of preparing, training for and inciting terror acts will now be put before parliament when MPs return from their summer break in October.
Meanwhile, the debate over highly controversial control orders has also been, temporarily, put to one side.
The prime minister will now underpin that new consensus at meetings with both Tory leader Michael Howard and the Liberal Democrat's Charles Kennedy.
He is also to meet members of the Muslim community and intelligence and police chiefs to hear what changes they believe are necessary, and how soon.
He will repeat his message to the Muslim leaders that they must help combat extremists with deeds as well as words.
But, while there is clearly a cross-party will to support any measures that might prove effective, there were reservations about the proposed laws which, presumably, have been addressed.
For example, the Liberal Democrats were concerned about the way "indirect incitement" might be defined, fearing it could be so wide as to encroach on legitimate free speech.
Clarke has laws planned for autumn
The Tories, meanwhile, are supporting the proposed new laws but wanted further debate about the possibility of allowing phone tap and other intercept evidence to be used in court.
The fine detail about what is actually being agreed will come later but, for the moment the prime minister has his longed for consensus.
The new laws are on target for the autumn, despite some suggestions they might be pushed through more quickly, although the prime minister has reserved the right to seek swifter action if requested by the police and security services.
But with the Commons set to rise on Thursday for the long summer break, time is short.
Commons security to be tightened
The Commons can always be recalled during the break, although the large amount of building work scheduled for the recess - ironically to tighten security in the palace of Westminster - would make it logistically difficult.
And that is leading many MPs believing that, barring any pressing demands from the security services, it may well be better to let the parliamentary process run to avoid any possibility of ill-thought out or badly drafted legislation from getting onto the statute books.
Perhaps the more difficult task ahead for the prime minister is his attempt, with the Muslim community, to tackle the root cause of the terrorism.
Mr Blair believes Muslim leaders can prove central in combating the "evil ideology" driving the terrorists.
His task is to win action from the community while not appearing to lay the blame for the bombings at its door.