The men were among five arrested on Friday, May 3, as part of an ongoing terrorism investigation.
According to PA, reports suggest the Israeli embassy in Kensington, west London, may have been the intended target, although police have not confirmed this.
The suspects include a 29-year-old man from Swindon, a 46-year-old from west London, a 29-year-old from Stockport, a 40-year-old from Rochdale, and a 24-year-old from Manchester.
According to the Metropolitan Police, four of the men were detained under the Terrorism Act and can be held until Saturday, May 17, after officers were granted warrants for further detention.
The fifth man, held under the Police and Criminal Evidence Act, has been released on conditional bail until later this month.
While press reports, including from The Times, have named the Israeli embassy as the likely target, the Met has declined to comment further.
Commander Dominic Murphy, head of the Met’s Counter Terrorism Command, described the case as a “significant and highly complex investigation”.
“Our officers and staff continue to progress what is a significant and highly complex investigation,” he said. “We are working incredibly hard with public safety at the forefront of our ongoing efforts.”
He urged the public not to speculate or circulate unverified information: “We have clear and critical reasons for not providing further details at this time.
“As soon as we can, we will look to share further information with the public.”
Searches are being carried out at several addresses across Greater Manchester, London, and Swindon, with the Met working closely with local police forces.
Commander Murphy added: “As always, I would ask the public to remain vigilant and if they see or hear anything that concerns them, then to contact us.”
Separately, in another national security investigation, three Iranian men were arrested in north London on May 3 under the National Security Act 2023.
A fourth man, also Iranian and suspected of “foreign power threat activity”, was arrested in the same area the day before.