London (CNN) -- 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."