Prime Minister Boris Johnson on Monday said Britain would "not be cowed by terrorism" after a homemade bomb destroyed a taxi outside a hospital in Liverpool, killing a passenger.

"We will never give in to those who see to divide us with senseless acts," he told a Downing Street news conference as police probed the motive behind the attack.

Police in northwest England on Monday said they were treating a deadly blast outside a hospital in Liverpool as a "terrorist incident" involving a homemade bomb that was reportedly foiled by a quick-thinking taxi driver.

Russ Jackson, in charge of counter-terrorism policing in the region, said the motivation for Sunday's blast in a taxi was unclear.

But he said the improvised explosive device, which ignited in the cab, turning it into a fireball, was "built by the passenger" who died.

The explosion outside the Liverpool Women's Hospital came just minutes before a Remembrance Sunday service at nearby Liverpool Cathedral.

That has prompted speculation the event was the intended target.

Jackson told a news conference: "We cannot at this time draw any connection with this but it is a line of inquiry, which 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."

Three men aged 21, 26 and 29 were arrested under the Terrorism Act soon after the explosion in the nearby Kensington area of the city and were taken for questioning.

A fourth man, aged 20, was detained earlier on Monday, Jackson said, adding that "significant items" had been found at a second address in Sefton Park, near Kensington.

- Remarkable escape -

The blast and fireball sent thick smoke into the air just seconds before Britain fell silent in tribute to its war dead and military veterans at 1100 GMT.

There was immediate praise for the taxi driver, who reportedly locked the passenger -- a man -- inside the cab after growing suspicious about his intentions.

The passenger had wanted to go to the annual service at Liverpool's Anglican cathedral, according to UK media quoting investigators and friends of the cabbie.

But road closures forced the taxi to detour and they ended up at the nearby hospital, where the bomb went off just after the driver had escaped, the Daily Mail reported.

Prime Minister Boris Johnson said moments before the news conference that it would be premature to comment in detail about the incident, with the investigation ongoing.

"But it does look as though the taxi driver in question did behave with incredible presence of mind and bravery," he told reporters in London.

Liverpool Mayor Joanne Anderson said: "The taxi driver, in his heroic efforts, has managed to divert what could have been an absolutely awful disaster at the hospital.

"We knew that the taxi driver had stood out and locked the doors, we knew that early on," she told BBC radio, while also warning against further speculation.

Jackson gave few details but said the taxi driver picked up the passenger from the Kensington area and was asked to be taken to the hospital.

"As the taxi approached the drop-off point at the hospital, an explosion occurred from within the car. This quickly engulfed it in flames," he added.

"Remarkably, the taxi driver escaped from the cab. He's been treated for his injuries that he sustained and he's now been released from hospital."

- 2,000 at cathedral -

Some 2,000 people attended the religious service of remembrance, one of the biggest outside London, according to the Liverpool Echo newspaper.

The event concluded with a military parade on the closed roads outside the cathedral.

Senior Conservative politician Oliver Dowden said the driver's actions contrasted with "the cowardice of terrorist attacks."

"Clearly we'll have to see exactly what happened there," the ruling party's co-chairman told Sky News, stressing reports of the driver's response had to be confirmed.

"But if that is the case, that's another example of true bravery and courage," Dowden said.

The scene at the hospital remained cordoned off on Monday, as did the streets around the two properties under investigation, where forensics officers in white suits were seen.

The domestic intelligence service MI5 is also assisting in the investigation, according to The Guardian newspaper and BBC.