Gordon Brown is being urged to scrap, or at least postpone, plans to partially privatise Royal Mail in the face of a growing revolt by Labour MPs.

Senior ministers have told Mr Brown that he will almost certainly have to rely on Conservative votes to push the plans through the House of Commons. But Lord Mandelson, the Business Secretary, wants to press ahead with the sale and will today step up efforts to win over hostile MPs.

About one hundred Labour MPs have signed a motion opposing the part-privatisation. The issue has prompted the resignation of one parliamentary aide and several more are said to be threatening to quit.

The Conservatives are hoping to take advantage of Labour's divisions during a Commons debate on Wednesday. They will try to force a vote on the Royal Mail sale.

Lord Mandelson will face questions over the postal service's future when he addresses a meeting of Labour backbenchers today. He is determined to press ahead with the sale of about a third of the postal service. “There is no plan B,” said one Whitehall official.

The sale was recommended in an official report before Christmas. The Hooper Review said the Government should clear the way for a joint venture with a private company by plugging a £7 billion deficit in the Royal Mail pension scheme. Lord Mandelson is believed to be in favour of implementing the recommendations quickly before the rebellion has a chance to gather further strength.

He has all but given up hopes of winning union support amid threats from the Communication Workers Union (CWU) to sever links with Labour and he believes MPs can be persuaded to back the plans.

The CWU has released the results of a poll that it said showed public opposition to any sale. Billy Hayes, CWU general secretary, said: “The public is overwhelmingly opposed to government plans to privatise part of Royal Mail. This is a deeply unpopular move, which would damage a trusted public service.

“We urge the Government to take responsible action and respond to the justified concerns of UK citizens who do not want to see this valuable public asset carved up and sold off.”

Dave Ward, deputy general secretary, added: “Royal Mail is a profitable public company with a dedicated workforce and unmatched public trust. Why would you gamble this away on an unpopular and unproven part sell-off? A huge majority of the public is against this idea.”

Pat McFadden, Minister for Postal Affairs, said: “Privatisation is not the Government's policy. Our proposals will maintain a publicly owned Royal Mail and safeguard the vital services it provides. We are proposing a joint venture with a postal operator that has a proven track record in transforming a postal business.

“Royal Mail is facing huge challenges, with falling mail volumes, a rising multibillion-pound pension deficit and an urgent need for improved efficiency through further automation. A joint venture, action on the pension deficit, and a new regulatory regime are together the way to transform Royal Mail and secure its future in public ownership.”

A Royal Mail spokesman said: “We firmly believe that a joint venture with the right minority partner, along with the Government tackling the historic pension deficit and being regulated as part of the wider communications market, will help to secure the future of the one-price-goes-anywhere Universal Service.”

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