The government has disputed claims that Britain it is not ready to deal with a major terrorist attack.
Concrete blocks have been placed around Westminster
Home Office minister Lord Falconer said on Saturday the UK was "resilient" against any such assault.
But two parliamentary committees warned that local planning is inadequate.
The Defence Select Committee suggested a US-style national "homelands security adviser" to oversee terrorist defence measures should be appointed to take the pressure off the home secretary.
Lord Falconer said there was no need and the government was doing "everything appropriate".
"I am utterly confident that we are taking the right preventative steps and that we are taking the right steps to be ready if a terrorist attack occurred," he told BBC Radio 4's Today programme.
The MPs on the influential committees pointed to the contrast between other countries' preparedness and the UK's state of readiness.
Australia, for instance, recently completed a three-day counter-terrorism training exercise which included a mock car bomb.
And earlier this month, Chicago and Seattle saw one of the biggest homeland security rehearsals ever staged in the US.
It cost an estimated $16m and involved 8,500 people in the US and Canada.
A similar rehearsal of procedures in the UK, at Bank tube station in London, was postponed before the war.
Lord Falconer said it would go ahead "as soon as practical" but the Science and Technology Select Committee urged the government to "step on the accelerator".
Chairman Ian Gibson, whose committee watched the exercises being carried out in the US, said the Americans had a "professional " approach to the threat.
"We really ought to step on the accelerator and open the whole debate up, and do more to reassure the public," he told Today.
We should be further down the line than we are by now
Terrorism expert Dr Magnus Ranthorpe, of St Andrews University, said the UK was on its highest terrorism alert and a "raging secret intelligence war" had identified two specific threats: Chemical agents and from lorries loaded with gas cylinders.
Lessons learned by other countries who have held terrorism exercises included that quarantine scenarios sparked violence and volunteers were better at responding than armed guardsmen.
The Fire Service believes the new date for a mass exercise in the UK could be as late as September.
Ross Neil, London regional chairman of the Fire Brigades Union, said: "We should be further down the line than we are by now."
Home Secretary David Blunkett promised in March that London's ability to respond to a catastrophic terror attack - covering mass-evacuation and decontamination - would be tested "within weeks".
Further exercises to test the UK's preparedness for attacks on flood defences and the national gas supply were also promised.
Security has been visibly tightened in the UK.
Concrete blocks have been positioned around the Houses of Parliament in London.
There has been a promise of more visible policing at Heathrow airport. Tanks were deployed at the airport for a few days in February.