The onlooker said two males jumped a red light before crashing a £50,000 Mercedes.
Arun Pullen, 22, said: "Tom must have been walking down the road. He went off like a shot in pursuit and looked furious."
He added: "I asked Tom what happened and he told me he chased him through my back garden and caught him around the block - but the route was like an assault course."
The Batman and The Revenant star, who recently co-wrote and appeared in BBC drama Taboo, then reportedly performed a citizens arrest on one of the suspects.
Two suspects were detained in connection with the theft, the newspaper said.
Mr Pullen's girlfriend, Kalisha, a fan of the actor, said: "There was no mistaking him."
A spokesman for the actor declined to comment.
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