The Christian Legal Centre (CLC), which is supporting Core Issues, welcomed the judge's criticism of TfL's "unfair" procedures.
"Coming on the heels of the 'BA cross' judgment in the European Court, this is another important victory for Christian freedoms and a stinging rebuke for Boris Johnson and TfL," said CLC's director Andrea Minichiello Williams."Blatant discrimination will not be tolerated by the courts."
She added: "This judgment exposes that bus adverts placed by Stonewall and the British Humanist Association were in clear breach of TfL's own guidelines yet they were allowed to run, even though they proved to be highly controversial at the time."Then, as soon as a Christian group responds to Stonewall's provocation and dares to challenge the reigning political orthodoxy, the message is banned.
"This case demonstrates the huge asymmetry and censorship that characterises public debate at the moment."Some people choose not to act on same-sex attraction. They should not be ostracised for doing so but helped, if that is what they choose. Mike Davidson and Core Issues Trust want to help those who experience same-sex attraction but would prefer to change that."
Ben Summerskill, the chief executive of gay rights group Stonewall said:
"Many people will be pleased by today's decision.
"Had these voodoo 'gay cure' adverts appeared in the pages of the Spectator or the Daily Telegraph it's unlikely there would have been complaints.
"But in a city where over half of gay young people face bullying at school, and where tens of thousands of gay people are subjected to hate crimes every year just because of the way they were born, it's perfectly proper for a mayor to object to the use of such advertising in an iconic public setting."
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".
The Mayor of London had decided to ban a controversial "gay cure" bus advert by a Christian group.
The ad read: "Not gay! Ex-gay, post-gay and proud. Get over it!" and Boris Johnson condemned it as "offensive to gays".
The Core Issues Trust Christian charity claimed that Boris Johnson was "politically driven" when he intervened to block the ad, but today a judge ruled that he did not abuse his position as chairman of Transport for London (TfL) when he imposed the ban.
Mrs Justice Lang, sitting at London's High Court, ruled that TfL's process in introducing the ban "was procedurally unfair, in breach of its own procedures and demonstrated a failure to consider the relevant issues".
But that was outweighed by factors against allowing the ad, including that it would "cause grave offence" to those who were gay and was perceived as homophobic, "thus increasing the risk of prejudice and homophobic attacks", said the judge.