Landmark plans to legalise gay marriage got the green light in the Commons, despite a majority of Tories failing to support the Government.
The Prime Minister will read the letter delivered to Number 10, take their views on board, but not change his mind over gay marriage.
Many Conservative MPs just do not understand the move when the tax measure is in the Coalition Agreement.
Gay marriage has become legal in Britain after the bill was granted Royal Assent by the Queen.
Current laws on marriage do not discriminate against homosexual people because they are free to marry someone of the opposite sex according to Lord Tebbit.
The Tory former cabinet minister said: "This Bill is promoted as a measure to end discrimination against homosexuals, but the present law of marriage does not discriminate against homosexuals.
"The rights of a homosexual man are identical to mine. Subject to the laws on incest and bigamy we are both free to marry a woman.
"Neither he nor I may marry another man. Our positions are identical.
"If it were to be held that the wish of a homosexual man to marry another homosexual man being thwarted by law was a proof of discrimination, then the law forbidding polygamy would equally be proof of discrimination.
"And therefore we should move undoubtedly on the basis of the arguments that have been put forward to marriage of one man to two women or more or a woman with more than one man."
He said the Bill would introduce a "real and novel form of discrimination" as there was no definition of what would amount to consummation or adultery in a same-sex marriage.
Religious peers have lent their weight to the same-sex marriage bill being debated in the House of Lords.
Baroness Neuberger, a senior rabbi at West London Synagogue and independent crossbench peer, said marriage was a "social construct" and had not always been between one man and one woman.
"I expect the first days after this becomes law, as I hope it does, to consist of marriage after marriage in my synagogue bringing joy and equality and renewed commitment to people who until this point have been denied it," she said.
Baroness Richardson of Calow, a Methodist minister and independent crossbench peer, said: "I believe in marriage. I believe that marriage is the bedrock of our society and brings stability to our communities.
"I believe that marriage is the best place where children can be nurtured and it is for those reasons that I will support this Bill."
Liberal Democrat Baroness Barker has told peers she had had a female partner for many years and strongly welcomed the Bill.
Lady Barker said the legislation reflected "the wishes of people who don't today just want to tolerate the views of lesbians and gay men but want to celebrate and support them as people in their own right."
She said: "I look forward to joining with people on all sides of this House to ensure that gay people and their families are afforded the dignity and respect that others take for granted and that families, faiths and communities can grow stronger together as a result."
Lord Chris Smith has spoken about how civil partnerships, "still labels our lesbian and gay relationships as somehow just a little second-class."
Lord Smith is often credited as the first openly gay MP and told the House of Lords tonight; "I happen to be gay...I am also a Christian and I believe in a loving, accepting, generous God who wants to include people not reject them."
Speaking as part of the debate on the Marriage (Same Sex Couples) Bill Lord Smith said: "Quite simply this is about love, commitment and mutual respect."
An Independent Peer has urged the House of Lords to block controversial plans to allow gay marriage after a bitter battle in the Commons.
Lord Dear demanded that the Marriage (Same Sex Couples) Bill should be refused a second reading.
Lord Dear warned that the "ill-considered Bill seeks to overturn centuries of tradition, heedless of public opinion and the views of religious leaders, and blind to the laws of unintended consequences".
Lord Dear also warned the Bill could be "counter-productive" in promoting tolerance for homosexual relationships.
"I fear the Bill, should it become law, could well create such opposition to homosexuals in general that the climate of tolerance and acceptance in this country, that we have all championed and supported and seen flourish over the years, could well be set back by decades."
But for the Government, Baroness Stowell of Beeston hailed the legislation as a "force for good" which would strengthen the institution of marriage.
More than 90 peers are due to speak in the debate which is scheduled to continue late into tonight and overspill into tomorrow's business when the crucial second reading vote will be taken.
Responding to last night's vote on gay marriage at Prime Minister's Questions, David Cameron said:
I'm a marriage man. I'm a great supporter of marriage. I want to promote marriage, to defend marriage, encourage marriage. And the great thing about last night's vote is that two gay people who love each other will now be able to get married and I think that's an important advance.
After MPs backed plan to legalise gay marriage by 400 votes to 175 on Tuesday, Virgin Holidays capitalised on the opportunity to advertise its travel offers by tweeting this picture:
Culture Secretary Maria Miller has suggested the Conservative rebellion on plans for gay marriage came as no surprise to the Government.
Tonight's Conservative rebellion on gay marriage shows the Prime Minister's political strategy to rebrand or redefine his party was "inappropriate", according to a leading Tory MP.
Ministerial aide David Burrowes, one of the leading opponents of the plans to legalise same-sex marriage, said it was "unprecedented" for more than half the party to fail to support a Government Bill.