Transport for London had refused to carry the ad on the grounds that it was "likely to cause widespread or serious offence to members of the public", and it contained "images or messages which relate to matters of public controversy and sensitivity".
Today the judge backed the TfL stance, despite her finding that there had been unfairness in its procedures.
The judge said TfL had applied its advertising policy "inconsistently and partially", but its refusal to display the gay ad was "justified and proportionate, in furtherance of the legitimate aim of protecting the rights of others".
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A lamp in the tower which houses Big Ben is to be switched off for the first time in more than 70 years.
Sir Bruce entertained audiences for more than seven decades.
Work in the tower will also pause over the bank holiday weekend.