The bill will now move to the House of Lords, whose approval is also required. Members there are expected to hold their first debate in July.
If approved, the law is expected to take effect in 2015, and enable same-sex couples to get married in both civil and religious ceremonies, provided the religious institution they choose consents.
Such a law also would allow couples who had previously entered into a civil partnership to convert their relationship to a marriage.
Developing story, check back for updates.
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