"The Attorney General acted in this regard completely independent of government and [in] his independent public interest capacity," the Metropolitan Police said in a joint statement with Goldsmith's office.
The BBC had argued that it should be allowed to report the story as a matter of public interest.
Police have been investigating allegations that Blair's Labour Party and other political parties had nominated people for seats in the House of Lords, parliament's upper house, in return for funding since March last year.
Lord Levy, a Labour Party fundraiser and Blair's Middle East envoy, was arrested in January on suspicion of conspiracy to pervert the course of justice, signalling that the inquiry had moved beyond the funding scandal. He also arrested last year.