Investigators said they were treating Sunday’s explosion – which killed the suspected bombmaker and injured the cab driver – as a terrorist incident but that the motive was unclear.
Counterterrorism police on Monday evening named the dead man as 32-year-old Emad Al Swealmeen.
They did not give further details although the Press Association and other media reported that he had not been on the radar of the security services.
The Joint Terrorism Analysis Centre raised the UK threat level from substantial – meaning an attack is likely – to severe, meaning it is highly likely, following the country’s second fatal incident in a month.
Conservative MP David Amess was stabbed to death in October in what police said was an act of terrorism.
Prime Minister Boris Johnson condemned the “sickening attack” at Liverpool Women’s Hospital and told reporters that the British people “will never be cowed by terrorism”.
“We will never give in to those who seek to divide us with senseless acts of violence,” he said.
The male passenger in a taxi was killed and the driver injured when a blast ripped through the vehicle as it pulled up outside the hospital on Sunday morning.
Russ Jackson, the head of Counterterrorism Policing in northwest England, said the explosion was caused by “the ignition of an explosive device” that was brought into the vehicle by the passenger.
Three men in their 20s were arrested elsewhere in the city on Sunday under the Terrorism Act and a fourth was detained on Monday.
All are believed to be “associates” of the dead passenger, police said.
Suspicions about a motive for the explosion have been aroused by the timing – just before 11am on Remembrance Sunday, the moment when people across the UK hold services in memory of those killed in wars.
Jackson said investigators had not found a link to remembrance events “but it is a line of inquiry we are pursuing”.
“Although the motivation for this incident is yet to be understood, given all the circumstances, it has been declared a terrorist incident,” he said at a press briefing.
He said the passenger had been picked up by the taxi a 10-minute drive away and asked to be taken to the hospital, where the explosion occurred.
The driver, named by local media as David Perry, managed to escape from the car.
He was treated in the hospital and released.
Police said officers had searched two addresses in the city linked to the passenger – one where he had lived and a second he had recently rented – and found “significant items” at the latter.
Officers performed a controlled explosion “as a precaution” as part of the investigation.
Liverpool Mayor Joanne Anderson said the taxi driver had locked the doors of his cab so the passenger couldn’t leave.
Police did not confirm that account.
“The taxi driver, in his heroic efforts, has managed to divert what could have been an absolutely awful disaster at the hospital,” Anderson told the BBC.
The prime minister also said the driver appeared to have behaved “with incredible presence of mind and bravery”.
The UK’s official terrorism threat level was lowered from “severe” to “substantial” in February.
It has been at severe most of the time since 2014, briefly rising to “critical” amid a spate of violent attacks in 2017.
The Joint Terrorism Analysis Centre sets the threat level based on intelligence about international terrorism at home and overseas.