Across Europe and the US support for same-sex marriage is growing, and for a simple reason: it is consistent with democracy's promise of equal rights for all people. As long as government is in the business of handing out marriage licences, all couples – regardless of their sexual orientation – deserve equal status in the eyes of the law.

I believe that it is only a question of when – not if – same-sex marriage is accepted as a normal and legal part of democratic societies. Here in the US, the change is happening rapidly. Two years ago, I helped lead the push for same-sex marriage in New York, and we were able to pass a law with bipartisan support.

At the time, we debated many of the questions that the UK parliament has been considering over the past weeks and months – including whether churches would be forced to perform same-sex marriages and whether "civil unions" are enough for same-sex couples. In the end, a majority of our legislators agreed that civil unions would relegate same-sex couples to second-class status – and that in approving marriage licenses, government should not discriminate between sexes. In addition, the law was written to ensure that no church would be forced to solemnise a marriage in contravention of its beliefs. And since the law has passed, none has.

Religious tolerance is a vital part of a democratic society. But religious rules should never dictate society's laws. Some religions prohibit eating pork. Others prohibit drinking alcohol. Others prohibit divorce. That is their right. But we reject any attempt to impose those prohibitions on society, because the freedom to engage in those activities should be no less protected. The same is true of same-sex marriage.

New York City embodies America's commitment to freedom and opportunity, diversity and tolerance, and that is why we remain such a magnet for immigrants, visitors and investors. People want to live in places where they are free to be themselves – to practise their religion as they wish, to express their political views as they wish, and to love and marry whom they wish.

Cities and countries that actively protect those freedoms will attract talented and creative people who wish to live freely, fostering a culture – and economy – that is stronger for it. As a mayor, I know that legalising same-sex marriage has sharpened New York City's competitive edge in the global economy, because it has made us an even more attractive place to live and work – not just for gay men and women, but for all people who want to live in a tolerant and free community. And as someone whose company is building a new European headquarters in London, I can say that same-sex marriage would make the UK an even more attractive place for companies to do business, because freedom attracts talent.

In America, support for same-sex marriage is building far beyond New York. Twelve of our 50 states have now legalised same-sex marriage. About one-fifth of all Americans now live in a place that has legalised same-sex marriage. In Washington, a majority of US senators have expressed support for marriage equality. And when President Obama said last year that he believed that same-sex couples should be allowed to marry, the American people did not vote him out office, even though some suspected it would hurt his re-election campaign.

It did not – because, as polls here show, a majority of Americans believe that same-sex marriages ought to have the same legal recognition as traditional marriages. Among younger Americans, it isn't even close: more than 80% of 18- to 29-year-olds support the freedom to marry. They will define the future. And just as young civil right activists in the 1950s and 1960s ended decades of discriminatory laws against African-Americans, today's young people will do the same for gays and lesbians.

Britons and Americans are beginning to see marriage equality for what it is: the reasonable next step in a shared history that includes extending suffrage to women and creating legal protections prohibiting discrimination. As the House of Lords votes on the issue, I hope its members will look to the future – and decide on which side of history they want to be.