Police in the Northern English city of Liverpool have released without charge four men arrested under terrorism laws, following a bomb explosion outside Liverpool Women's Hospital on Sunday.

The four-three aged 21, 26 and 29, detained on Sunday, and a 20-year-old man who was held on Monday-were all arrested in the Kensington area of the city.

"Following interviews with the arrested men, we are satisfied with the accounts they have provided and they have been released from police custody," said Assistant Chief Constable Russ Jackson, head of Counter Terrorism Policing North West.

A man killed at the site of the explosion, when a homemade device went off in the back of a taxi, has been named as 32-year-old Emad Al Swealmeen, described by the BBC as a refugee from Syria, who converted to Christianity in 2017.

Police have been conducting searches at a property he rented in Rutland Avenue near Sefton Park, in the south-east of the city, which they said is "becoming central to the investigation", and from which he was picked up by taxi driver David Perry on Sunday morning.

Perry, who has been hailed as a hero for his swift thinking in locking the passenger in his taxi when he saw he was carrying an explosive device, received hospital treatment but has since been discharged.

His wife posted a message on social media saying "he is doing ok but is extremely sore and just trying to process what's happened… he is, without doubt, lucky to be alive …h(huán)ow he managed to escape is an utter miracle."

What was described as "important evidence" has been found at the rental address, and Jackson added: "We have made significant progress since Sunday morning and have a much greater understanding of the component parts of the device, how they were obtained and how the parts are likely to have been assembled."

The explosion took place around 11 am GMT on Sunday morning, the same time that Remembrance Sunday memorial services were being held across the whole country.

As a result of what happened, Britain's Joint Terrorism Analysis Centre has raised the United Kingdom's terror threat to "severe", which means an attack is highly likely, one level below critical, which means an attack is highly likely in the near future.

Malcolm and Elizabeth Hitchcott, who had taken the dead man in to live in their house before he rented his own property, told the BBC of their shock at hearing the news.

"We're just so, so sad. We just loved him, he was a lovely guy," said Hitchcott.

"He lived here for eight months, and we were living cheek by jowl… there was never any suggestion of anything amiss," her husband told ITV News.