The suspect was arrested in the early hours of Tuesday on suspicion of arson with intent to endanger life, according to the Metropolitan Police.
Emergency services were called to fires at the doors of two homes in north London within 24 hours of each other - one just after 1.35am on Monday in Kentish Town and the other on Sunday in Islington. Both properties are linked to Sir Keir.
Detectives were also checking a vehicle fire last Thursday on the same street as the Kentish Town property to see whether it is connected.
Part of the area was cordoned off as police and London Fire Brigade (LFB) investigators examined the scene, while charred ground, apparent evidence of a fire, could be seen on the street.
Neighbours described hearing a loud bang and said police officers were looking for a projectile.
The prime minister is understood to still own the home, which was damaged by fire on Monday, but nobody was hurt. Pictures showed scorching at the entrance to the property.
Sir Keir used to live there before he and his family moved into 10 Downing Street after Labour won last year's general election. It is believed the property is being rented out.
In the early hours of Sunday, firefighters dealt with a small fire at the front door of a house converted into flats in nearby Islington, which is also linked to the prime minister.
In a statement, police said: "As a precaution and due to the property having previous connections with a high-profile public figure, officers from the Met's Counter Terrorism Command are leading the investigation into this fire.
"Enquiries are ongoing to establish what caused it. All three fires are being treated as suspicious at this time, and enquiries remain ongoing."
The prime minister's official spokesman said: "I can only say that the prime minister thanks the emergency services for their work and it is subject to a live investigation. So I can't comment any further."
Kemi Badenoch has condemned the suspected arson attacks.
Writing on X, the Conservative leader said: "This is a shocking incident. My thoughts are with the prime minister and his family. No one should face these sorts of threats, let alone people in public service.
"It's an attack on our democracy and must never be tolerated."
Shadow justice secretary Robert Jenrick told Sky News on Tuesday: "It's important that the prime minister and anyone in public life has their family, their homes, protected.
"It is absolutely wrong, disgraceful, for any individual to take the kind of action that we saw against the prime minister's home."
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