The ruling in the High Court followed a trial over articles in the Daily Mirror that he claimed had portrayed him as a fraudster and made him “a laughing stock”. He was not in court for the ruling by Mr Justice Eady, who will assess damages in October.

McKenna, 42, whose self-help hypnotherapy business has a turnover of £2.5 million a year, said that he was devastated when the columnist Victor Lewis-Smith alleged that he had bought a “bogus” PhD from La Salle University in Louisiana for $2,615.

Under the headline “It’s a load of doc and bull”, Mr Lewis-Smith wrote: “I discovered that anyone could be fully doctored by Lasalle within months (no previous qualifications needed), just so long as they could answer the following question correctly: ‘Do you have $2,615, sir?’.”

The newspaper’s publisher, MGN, which denied libel and pleaded justification, called evidence from Mr Lewis-Smith’s co-writer, Paul Sparks, who said he was told by the university that he could obtain a doctorate for that fee within a matter of months and without undertaking any formal course.

The judge, who heard the case without a jury, said that the newspaper had not proved that the sting of the words complained of was substantially true.

McKenna was awarded his costs, estimated at £300,000, and the judge ordered the newspaper to pay an interim amount of £75,000.

Marcus Partington, head of MGN’s legal department, said: “We are dismayed about the judgment.”

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