Detectives are investigating the claims after six cars were torched at GP Motors in Eltisley Avenue, Newnham, which spread to the main showroom.
A group called the "Fire Cell" made the claim to have started the fire on the Cambridge Anarchists’ website.
Director Richard Palmer said the fire, which happened in the early hours of Tuesday (Oct 11) last week, could cost the 31-year-old firm £80,000.
Mr Palmer is appalled by the claims and believes there could be some truth behind them.
He told the News: "They knew that two cars had been torched and said they hoped the fire would spread to others, which it did, so it seems they have some knowledge about it.
"I am just angry about the whole thing. They have targeted the wrong people. We are a family business and we don’t have much money.
"I am a bit relieved it wasn’t anything personal but I am still angry that lives could have been put at risk."
The message by the Fire Cell on the anarchist website said: "Two cars at the GP Motors dealership in Newnham, Cambridge, were arsoned – we hope the flames spread to the others, bringing a roaring inferno to the quiet leafy streets."
"No one was outside, the only sign of the middle-class residents awake was the blue glow of TV screens from curtained windows!
"While the insurrectionary action cell had adrenaline pumping, joy in the heart, the moon shining bright above and the refreshing night air."
A message supporting the criminal action said: "Here at Cambridge Anarchists we doff our collective caps to the spirit of this action. There can be only more. Solidarity with the Fire Cell."
A Cambridgeshire police spokeswoman said: "We have been made aware of this information and investigations continue. At this stage no-one has been arrested in connection with the arson.
"We continue to urge people with information about those responsible to contact police."
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