There had been fears that Pride London, which also incorporates World Pride 2012, would be cancelled due to funding problems.
Ken Livingstone has called for Londoners to be united after claiming that it's the 'Muslims turn now' to be discriminated against.
Stonewall hustings at the Southbank
The majority of London's primary school teachers think they can not talk about homosexuality in the classroom.
A survey found only 11% of teachers knew they could discuss gay issues, such as same-sex parents, in front of children.
The polling by Stonewall reveals primary school teachers in London are significantly less likely than their peers across the country to know whether they are allowed to teach about lesbian, gay or bisexual issues.
It found 35% of teachers in Scotland, 29% in the rest of the south, 24% in the north and 22% in Midlands and Wales, knew they could talk about homosexuality.
Research by Stonewall shows that more than half (55 per cent) of gay young people experience homophobic bullying.
The Lesbian Gay and Bisexual charity says that if homophobic bullying goes unchallenged, it can have severe negative consequences for young people.
It says three out of five gay young people say homophobic bullying affects their school work and many have skipped school because of it. Homophobic bullying also impacts on young people's self-esteem and ambitions.
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."
The Core Issues Trust had asked the judge to rule that the charity was unlawfully denied the freedom to express its views on homosexuality.
Their advert had been intended as a response to a bus poster campaign by gay rights group Stonewall, which carried the message: "Some people are gay. Get over it!"
Paul Diamond, appearing for Core Issues, contended that the trust was equally entitled to express its view on the sides of buses, and to have its right to freedom of expression protected under Article 10 of the European Convention on Human Rights.
He said the Trust had nothing but "utter respect for people struggling with same-sex attraction" and denied that it was attempting to offer a so-called "gay cure".
A scaled down version of London's Gay Pride took place today, and despite the cutbacks, it went off without a hitch. There had been fears the event would be cancelled due to funding problems.
Despite fears that Pride London, which also incorporates World Pride 2012, would be cancelled due to funding problems, it has been a huge success.
Gay human rights campaigner Peter Tatchell, who helped organise the first Gay Pride in Britain in 1972, said that despite the problems and setbacks, the numbers at today's events were huge and the atmosphere amazing.
– Peter Tatchell, human rights campaigner
It's much more political than in previous years. The global human rights message is really strong for lesbian, gay, bisexual, and transgender freedom.
Nearly 80 countries still criminalise homosexuality with the penalties ranging from life imprisonment and even execution.
We are also celebrating 40 years of Gay Pride in Britain. In those last four decades we have won the appeal of nearly every anti-gay law. All that remains is to win same sex marriage."
Prime Minister David Cameron has also added his support for the event.
– Prime Minister David Cameron
The UK has been judged to be the best country in Europe in which to live if you're gay so it is great that World Pride is being celebrated here in London - especially during this Diamond Jubilee and Olympic year.
I'm very pleased that the Mayor of London has enabled the march and events in Trafalgar Square to go ahead and I want to thank all the volunteers who will be stewarding the event and contributing to it.
It is 40 years since people first marched in London calling for equal rights. Since then we've come a very long way and progress is still being made."
A scaled back version of Gay Pride is underway in Westminster.There had been fears that Pride London, which also incorporates World Pride 2012, would be cancelled due to funding problems.
I'ts kicked off without a hitch, with a walking procession from Baker Street to Whitehall. But there will be no floats or other vehicles involved.
This will be followed celebrations in Trafalgar Square until 6pm.
Soho is expected to be busy throughout the day.
London's gay world pride is taking place today - but it will be a scaled down version due to lack of funds.
Organisers say 5,000 people have signed up to participate in the procession in central London.
There will be a party in Trafalgar Square including a set from Boy George and R&B singer Deborah Cox.
However, because of a funding shortage, the event will not include floats or a street party in Soho.