The BBC had taken legal action on Wednesday to block publication by HarperCollins of an autobiography that would unmask the faceless mystery driver.
It argued he is bound by a confidentiality agreement and revealing who he is would spoil viewers' enjoyment of the popular BBC program.
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But after more than a day of legal submissions in private before Justice Morgan in London, lawyers for HarperCollins emerged to say the case had concluded in their favour.
Solicitor Robin Shaw said: "The judge has said he is not going to grant an injunction in this case. Reasons are to follow and will be given in a private judgment."
He added there was unlikely to be a further public statement or another court hearing on Wednesday.
A spokeswoman for the BBC said Wednesday's judgment did not prevent it from pursuing the matter to a full trial of the issues.
