Britain had raised the threat level to "critical" - meaning another attack was expected "imminently" - on Saturday, after the failed double car bombing in London on Friday and a botched attack at Glasgow airport on Saturday.
Earlier on Wednesday, Gordon Brown, the prime minister, announced that Britain was to expand checks on skilled migrant workers seeking to enter the country.
Brown's statement comes following the arrest of suspects from countries including Iraq and Jordan.
At least six of the suspects are believed to be doctors, including a Jordanian neurosurgeon and an Iraqi physician.
One suspect was detained in Brisbane as he prepared to leave the country.
"It is vitally important the message is sent out to the rest of the world that we will stand strong, steadfast and united in the face of terror," Brown, who succeeded Tony Blair as the British premier last week, said.
As well as expanding background checks on skilled workers, Brown said Britain would widen a worldwide "watch list" of potential terrorists to help warn other countries.
Meanhwhile, a senior British detective was heading for Australia to question one of the eight suspects.
The first arrests in the investigation were made on Saturday after police apprehended the two men who had driven a car into the main terminal at Glasgow airport.
One of them, who remains in hospital in a critical condition from the burns he suffered, has been identified by British television as Khalid Ahmed.
The other Glasgow suspect has been named as Bilal Abdulla, an Iraqi doctor.
On Sunday, police arrested a 26-year-old man and a 27-year-old woman. Believed to be a Jordanian surgeon named by officials in Amman as Mohammed Jamil Abdelkader Asha, the man and his wife are now being questioned in London.
A fifth suspect, a 26-year-old man, was arrested in Liverpool. On Sunday, two other men, aged 25 and 28, were detained outside Glasgow.