It is challenging the decision of the Mayor of London, Boris Johnson, after Transport for London (TfL) banned an advert that Core Issues Trust wanted to put on London buses in 2012.
The Christian charity has been told to pay court costs of more than £100,000 for the legal battle over the advert that said "Not Gay! Ex-Gay, Post-Gay and Proud. Get over it!"
It was a direct response to a pro-LGBT campaign by Stonewall displayed on buses, that read: "Some people are gay. Get over it!"
The Stonewall slogan appeared on 1,000 buses however the Core Issues advert was banned hours before it was due to appear, following media pressure and intervention from the Mayor of London.
The Christian charity insists this was a challenge to the freedom of expression and will appeal the decision.
In 2013, the High Court ruled that TfL had applied its policy "inconsistently" and "partially" when it barred the Trust's bus adverts but permitted those of Stonewall.
Mrs Justice Lang upheld the ban on the Core Issues Trust advert, but said that TfL's decision-making was "procedurally unfair", "in breach of its own procedures" and "demonstrated a failure to consider the relevant issues."
Following the decision there was reports that the Mayor had personally instructed TfL to ban the adverts.
Core Issues took the case to the Court of Appeal which sent it back to Mrs Justice Lang in January 2014 to consider the new email evidence which she had not seen at the first hearing.
Before the 2012 Mayor of London elections, a judge asked the High Court to decide if Mr Johnson had took the decision based on political motivations.
But Mrs Justice Lang concluded that: "I consider that his response would have been the same, whether or not he was in an election campaign."
In a signed witness statement to the High Court, Boris Johnson then denied banning the adverts.
Mrs Justice Lang concluded in her judgment that "the dispute at the hearing about the correct meaning of the word 'instruction' was in danger of becoming a debate about semantics."
The Christian charity has been told to pay £100,000 to Transport for London.