Britain will not yield despite a sustained threat from people associated with al-Qaeda, Gordon Brown has said after the attempted car bombings.
The prime minister was speaking after a burning car driven into Glasgow Airport on Saturday was linked to two car bombs found in London's West End on Friday.
Five people have been arrested over the attacks - two at the airport, two later in Cheshire and a fifth in Liverpool.
Houses in Staffordshire, Liverpool and near Glasgow are also being searched.
Mr Brown told Andrew Marr on BBC One's Sunday AM it was "clear that we are dealing, in general terms, with people who are associated with al-Qaeda".
"It's obvious that we have a group of people - not just in this country, but round the world - who're prepared at any time to inflict what they want to be maximum damage on civilians, irrespective of the religion of these people who are killed or maimed are to be," he said.
Glasgow - Burning car driven into doors of Glasgow Airport on Saturday. Two people arrested at scene
London - Two car bombs that failed to detonate found in central London on Friday
Paisley - Controlled explosion carried out on car at Royal Alexandra Hospital
Cheshire - Man and woman arrested overnight on M6, then taken to London for questioning
Liverpool - Man arrested. Police searching two addresses
Houston - Police searching houses in village near Glasgow airport
Newcastle-under-Lyme - Police searching house in Staffordshire
Mr Brown also praised the "magnificent work" of police and security services and the public for being vigilant.
He said people still needed to be "constantly vigilant" against a "long-term and sustained threat".
He added: "We've got to separate if you like those great moderate members of our community from a few extremists who wish to practise both violence and inflict maximum loss of life in the interests of a perversion of their religion."
Home Secretary Jacqui Smith said the British public would not be "intimidated or let anyone stop us getting on with our lives".
Speaking after the government's emergency response unit, Cobra, held its fourth meeting in three days, she said a formal statement will be made in the Commons on Monday.
Speaking during a visit to Glasgow Airport, Scotland's First Minister Alex Salmond praised the efforts of the emergency services, and travellers for showing "great patience".
He said Scotland had not been complacent about such threats and preparations had been in place.
One of the suspects held at Glasgow Airport suffered severe burns and was taken to Royal Alexandra Hospital, in Paisley, where he is said to be in a critical condition.
A controlled explosion was later carried out at the hospital on a car, thought to be connected to the attack on Glasgow Airport, police said.
Scotland Yard said two people arrested on the M6 in Cheshire overnight - a 26-year-old man and 27-year-old woman - have been brought to London for questioning.
A spokesperson said Merseyside Police had arrested a 26-year-old man and were searching two addresses in the Liverpool area.
Staffordshire Police said its officers were involved in searches of addresses in Newcastle-under-Lyme with the West Midlands Counter Terrorism Unit and Met personnel.
The UK has moved to its highest level of terror alert - critical - after a Jeep Cherokee believed to have contained gas cylinders crashed into the main doors of Glasgow Airport's main terminal and burst into flames.
An eyewitness to the arrests in Cheshire, Peter Whitehead, told BBC News 24 that three unmarked police cars straddled the motorway and brought traffic to a halt.
Counter-terrorism police made the arrests hours after Strathclyde police had confirmed they were linking the attack in Glasgow with events in London and treating it as a "terrorist incident".
The Glasgow incident came after two Mercedes containing petrol, gas cylinders and nails were found outside the Tiger Tiger club in London's Haymarket and a nearby street on Friday, but the devices did not detonate.
BBC home affairs correspondent Danny Shaw said the decision to raise the UK's security level to critical on Saturday reflected concern that those responsible have the capability and intent to carry out further bombings.
He said the similarities between the attacks suggested they were carried out by the same individuals or by members of the same cell.
The critical threat level, the highest one possible, indicates terror attacks are "imminent".
Lord Stevens, Mr Brown's new terrorism adviser, has said the attacks signalled a "major escalation in the war being waged on us by Islamic terrorists".
He wrote in his column in the News of the World: "It is clear a loose but deadly network of interlinked operational cells has developed."
'CRITICAL' THREAT LEVEL
Critical - an attack is expected imminently
It is the highest of five threat levels under the new system which began in August 2006
It can be based on intelligence but in this case is understood to have been raised because previous attacks suggest risk
It is the second time the UK has been 'critical' under the system
He also said the "trick" of exploding one device and shortly afterwards igniting another to catch fleeing crowds was "textbook al-Qaeda".
The Met Police, meanwhile, have been increasing patrols and security for events in London over the weekend, including the Concert for Diana at Wembley Stadium.
The British Muslim Forum condemned the attempted attacks.
"We take the heightened security level extremely seriously and urge all of our communities to remain calm, be extra vigilant and report anything suspicious to the authorities," chair Khurshid Ahmed said in a statement.
"It is the duty of every British citizen to assist the police in safeguarding national security and ensuring the safety of all our citizens."
Police have urged anyone with information to phone the confidential Anti-Terrorism hotline number on 0800789321.