UK lawmakers took a big step Tuesday toward legalizing same-sex marriage, an issue that has prompted widespread rebellion within Prime Minister David Cameron's Conservative Party.

In a 400-175 vote, MPs approved the second reading of a bill legalizing such marriage, indicating a significant majority of members support the measure. However, it must go through several more stages before it can become law.

The bill faces another vote in the House of Commons and a vote in the House of Lords.

Before Tuesday's vote, three top party members appealed to Conservative MPs to get behind the controversial legislation in a letter published in the Telegraph newspaper.

The letter, signed by Chancellor George Osborne, Foreign Secretary William Hague and Home Secretary Theresa May, said that passing the bill is "the right thing to do at the right time."

The institution of marriage has evolved over time, the letter said, while "attitudes towards gay people have changed."

In a direct appeal to fellow party members, the trio added: "We believe that opening it up to same-sex couples will strengthen, not weaken, the institution. As David Cameron has said, we should support gay marriage not in spite of being Conservatives, but because we are Conservatives."

Their attitude was echoed by Kate Green, a Labour MP, during debate. Tuesday's reading was the first opportunity for lawmakers in the House of Commons to debate the bill in detail.

"By recognizing and extending the definition of marriage to reflect today's greater openness towards, and recognition of, same-sex relationships, the legislation does not weaken the institution of marriage. On the contrary, it takes it forward, it strengthens it. It helps to perpetuate it," she said.

The legislation passed the House of Commons with the support of lawmakers from Labour and the Liberal Democrats. The latter are in a coalition government with the Conservatives.

As drafted, the bill would enable religious organizations to choose to conduct same-sex marriages if they wish and includes provisions intended to make sure no religious organization or person is forced to do so.

The Church of England is among the religious bodies opposed to the legislation.

The bill would also allow same-sex couples to convert a civil partnership to a marriage and enable married transsexual people to gain legal recognition in their acquired gender without having to end their marriages.

A law recognizing civil partnerships in England and Wales was passed in 2004.

Tony and Barrie Drewitt-Barlow, who are already same-sex civil partners and have five children together, told CNN that it was important to them to be able to marry in front of their fellow churchgoers.

"We want to be able to go into our local parish church, where we are practicing Christians, and under the eyes of the Lord, get married," said Barrie Drewitt-Barlow.

"I don't want to go in front of a vicar or priest who doesn't want to do it; it's supposed to be the happiest day of my life. I want to be really happy and joyous when I get married to the man that I've been together with for 25 years."

His partner, Tony, said it was a question of equality.

"Marriage is all about the union of two people that love each other and want to bind that love in a relationship that lasts forever. And for me, it's about having that right for everybody, gay, straight or bisexual," he said.

"Whatever you are, if you love that person, then you should have the rights to be joined in matrimony with them."