Lord Waheed Alli, Labour peer and one of just a handful of openly gay Muslim politicians globally, has said he believes many peers who now oppose same-sex marriage “will probably repent later”.

In an interview with The Independent, Lord Alli argued that is was contradictory for the Church of England to clamour that the bill damages religious freedom, as their opposition to it puts limits on religious groups who want to perform same-sex marriages.

“They argue religious freedom except where they don’t like it,” he said. “They don’t want gay marriage – so that means the Quakers can’t have it or the liberal Jews can’t have it. They’re in a pretty hypocritical place.”

The current same-sex marriage debate reminds Lord Alli of the 1999 House of Lords debate on equalising the age of consent for same-sex relationships – a debate in which he became the first peer to come out as gay.

“I was called ‘sinful’, ‘disgraceful’ and ‘dirty’,” he said. “And that was in a debate in the House of Lords – it was awful. I’d only been there a few months. When the whip came back and reported that we’d lost by a huge number, I felt physically sick.”

Fortunately, the age of consent was lowered by Parliament Act in 2000. Some peers later said they regretted opposing the measure, and Lord Alli believes the same will be true for equal marriage.

“There are those who have deeply held religious views and then there is a second group who oppose now but will probably repent later,” he said.

“They were the type of people who voted against the equalisation of consent and regretted it. They are the people who voted against civil partnerships and regretted it. And I’ll believe they’ll vote against gay marriage and they’ll regret it in five years’ time.”

In an effort to change the minds of peers, Lord Alli said he had been lobbying fiercely on the issue. This included arranging a meeting with the Archbishop of Canterbury, Justin Welby.

“I said [to Archbishop Welby] that I knew there were people in the Church – such as the Bishop of Salisbury – who were supportive of gay marriage and I asked him if I went to see him and asked him to do a piece would he have your blessing? He said ‘Absolutely. And that goes for any bishop.’”

That exchange led to the Bishop of Salisbury writing a letter for Lord Alli, published in the Telegraph last week, in which he likened opponents of equal marriage to Christians who used the Bible to justify slavery and apartheid.

The Archbishop of Canterbury remains opposed to the legalisation of same-sex marriage, but sources say he and other Church figures are resigned to it. He is expected to push for amendments to the bill when it is voted on next week.

The House of Lords is due to hear the same-sex marriage bill on Monday and Tuesday.