A third man has been arrested over suspected arson attacks on two properties and a car linked to Keir Starmer.

The 34-year-old man was arrested on Monday morning in Chelsea, west London, on suspicion of conspiracy to commit arson with intent to endanger life, the Metropolitan police said.

The man was taken into custody. The arrest was made by counter-terrorism officers who are leading the investigation into three incidents.

One was a fire at the prime minister’s family home in north-west London, which he lets to his sister-in-law. The blaze was reported to police by firefighters in the early hours of 12 May. Police said damage was caused to the property’s entrance but nobody was hurt.

A car Starmer sold to a neighbour last year was set alight four days earlier on the same street.

On 11 May, firefighters dealt with a small fire at the front door of a house where the Labour leader is understood to have lived in the 1990s before it was converted into flats.

A 26-year-old man arrested on Saturday for the same alleged offence remains in police custody after a warrant of further detention was obtained at Westminster magistrates court. He is in police custody after detectives obtained a warrant of further detention.

The Guardian understands the second man was arrested on Saturday at Luton airport, where counter terrorism detectives believe he was trying to leave the country.

Roman Lavrynovych, a 21-year-old Ukrainian man and the first to be arrested over the incidents, has appeared in court charged with three counts of arson with intent to endanger life in connection with the fires.

Lavrynovych, of Sydenham, south-east London, was remanded in custody after appearing at Westminster magistrates court. He did not enter a plea. He will appear at the Old Bailey for a plea and trial preparation hearing on 6 June.

Anyone with information that could assist the investigation has been asked to contact the Met.