The Conservative grassroots rebellion over plans to equalise laws to allow gay and lesbian couples to marry has moved up a step with a group of party constituency chairmen and longstanding supporters taking their protest to Downing Street.

A letter signed by 22 current and former chairmen of local groups urges the prime minister to reconsider or at least delay the plans, which face a crucial vote this week.

With 303 Conservative MPs and more than twice that many parliamentary constituencies in the UK, the signatories officially represent a small proportion of the party grassroots party. But their intervention will be taken seriously with growing signs of unhappiness among Tory MPs and their supporters. Even MPs who support equal marriage laws report they are inundated with emails and letters objecting to the move and only a small handful are in support.

Sunday newspapers report that up to four cabinet ministers and potentially more than half of Conservative MPs are considering voting against the bill on Tuesday – which despite being a free vote would be an embarrassment to the Tory leadership and especially for David Cameron, who has been so closely associated with the proposal. No 10 claim the number of likely Tory no-votes is closer to 130 MPs. The bill is expected to pass with overwhelming support from Liberal Democrats and Labour.

In their letter, the constituency chairmen say: "Resignations from the party are beginning to multiply and we fear that, if enacted, this bill will lead to significant damage to the Conservative party in the runup to the 2015 election."

However Tim Montgomerie, editor of the Conservative Home party-supporting website, pointed to analysis of polls by YouGov showing opposition to equal marriage would only cost the party at most 1% of its total current estimated support at the next election, not including any votes it might win as a result of pushing through the measure.

The letter's signatories say there is a lot of public opposition. They argue civil partnerships already allow gay and lesbian couples to form legal ties, and warn the proposals do not give adequate protection for churches and teachers to refuse to conduct the ceremonies or teach pupils about them.

But they reserve their fiercest criticism for bringing forward the bill "without adequate debate or consultation with either the membership of the Conservative party or the country at large".

They add: "We are of the clear view that there is no mandate for this bill to be passed in either the 2010 Conservative manifesto or the 2010 coalition agreement and that it is being pushed through parliament in a manner which a significant proportion of the Conservative party members find extremely distasteful and contrary to the principles of both the party and the best traditions of our democracy."

A spokesman told the Guardian that although the bill was expected to pass on Tuesday they wanted the PM "to take the decision he'll slow the whole thing down". He added: "He could quite reasonably postpone the thing until after the general election."

In the Mail on Sunday, the education secretary, Michael Gove, has written in support of Tuesday's bill. His article represents possibly the most high-profile intervention in favour of Cameron's actions. "Nothing in my life has changed me more, matters more or influences me more than my marriage," writes Gove, and it has "brought me and brings me a happiness greater than any I had known before". He adds: "It's wrong to say to gay men and women that their love is less legitimate. It's wrong to say that because of how you love and who you love, you are not entitled to the same rights as others. It's wrong because inequality is wrong."

The culture minister, Ed Vaizey, insisted the vote would not tear the Tory party apart and claimed internal divisions were a "civilised debate".

"We'll see what happens in the vote on Tuesday. Various numbers have been bandied about, but what I would say is that it is good-natured division," he said on the Murnaghan programme on Sky News.

The former children's minister Tim Loughton agreed that it would not tear the party apart but warned the bill was "full of pitfalls" and would set MP against MP.

He told Murnaghan: "There's quite a lot of things that were in our manifesto which made it to the coalition agreement which we have yet to deliver, and yet gay marriage is something which we had no green paper, no white paper, no manifesto commitment of any party. It wasn't in the coalition agreement, and all of a sudden it is taking huge priority. It is going to take up a lot of parliamentary time and is going set MP against MP, and we don't need it."