The home secretary Jacqui Smith will update MPs on the terror threat and ongoing investigation later today.
The government has so far called for increased vigilance but stressed the need to allow the police time to investigate the two failed terror attacks on London and Glasgow.
Ms Smith was a surprise appointment as home secretary and commentators are waiting to see if she displays the same hard-line approach as her predecessor, John Reid.
So far Gordon Brown's rhetoric has displayed a more cautious response to the terror threat than the previous government's.
Shami Charkabarti, the director of human rights' group Liberty, praised Mr Brown's immediate response to the terror threat, saying he had been serious and reassuring and "so far no party politics".
George Bush has also praised the "very strong response" of Mr Brown's government.
The prime minister has said Britons will need to accept increased security measures, but whether this ultimately refers to security checks or new anti-terror legislation remains to be seen.
Speaking yesterday Mr Brown reiterated his support for extending the 28 day detention period and the creation of a single security budget. However he said these were "not an issue for today".
Interviewed on BBC's Sunday AM the prime minister said Britons would need to accept constant vigilance and increased security checks, but life should otherwise continue as normal.
As prime minister, Mr Brown said his first duty is to protect the safety and security of the British people.
He insisted withdrawing British troops from Iraq would not end the terror threat and instead the government must win the battle of hearts and minds.
Speaking ahead of her appearance in the Commons, Ms Smith said the government would pursue a cross-departmental approach to tackling the roots of terrorism.
She promised to work with David Miliband in the Foreign Office and Hazel Blears at the Community Department, playing down any immediate legislative plans within the Home office.
She said: "We are absolutely determined to, by working together, find not just the legislative but the other ways we can counter this terrorist threat."
However, she confirmed the government will introduce planned anti-terror laws before the end of the year. She said these would be produced following a consultation period with everyone of "good will" within the country.
Mr Brown is expected to meet with David Cameron to form a consensus on anti-terrorism legislation and the Tory leader has pledged to work "as closely as I can" with Mr Brown.
The Conservatives have now suggested they could support proposals to increase the 28 day limit on detention without charge.
Cross party support is also building for the use of phone tap evidence in court and reforms to allow police to question suspects after they have been charged.