Police have been given another 36 hours to question a man arrested in connection with suspected arson attacks on properties in London linked to Keir Starmer.

The 21-year-old was arrested early on Tuesday at an address in Sydenham, south London, on suspicion of arson with intent to endanger life. Police can now hold him until Friday morning.

The prime minister’s family home in north-west London, which he now rents out, a flat he once owned, and a car he previously owned were involved. Detectives are trying to determine if all three cases are linked.

None of the incidents led to injuries and police said “damage was caused to the property’s entrance” of the Starmer family home in Kentish Town.

Starmer, who lives with his family at his official residence in Downing Street, is understood to be renting out the four-bedroom house to his sister-in-law and her family.

At prime minister’s questions on Wednesday, Kemi Badenoch began by telling Starmer she was “horrified” to hear about the incidents. The Conservative leader added: “It is completely unacceptable, and I think I speak for the whole house when I say that it was an attack not just on him, but on all of us and on our democracy.”

Starmer replied: “I thank the leader of the opposition for her words about the attacks on me and my family, and many others for their kind messages in the past few days.”

Badenoch, he said, had messaged him personally “pretty well straight away” when the news emerged. He added: “She is absolutely right that it was an attack on all of us, on democracy and on the values that we stand for.”

Ed Davey, the Liberal Democrat leader, also offered Starmer his sympathies and support.