The Royal Mail could fall into foreign hands if trade unions continue to fight its flotation on the London Stock Exchange, the business minister, Michael Fallon, has warned.

Fallon said the government would sell Royal Mail to sovereign wealth funds or other foreign buyers if postal workers' campaign against a flotation in London makes an initial public offering (IPO) on the stock market difficult. He said numerous overseas buyers had already expressed "significant interest" in snapping up the 497-year-old postal service. "It's a great British brand with the Queen's head on it," he told the Observer. "We have already had quite a lot of interest in it."

He revealed that Royal Mail's boss, Moya Greene, had already embarked on a global roadshow promoting the postal service to sovereign wealth funds and foreign trade buyers as well as institutional investors based in the UK and overseas.

"Royal Mail have been testing investor appetite here, in Canada and the United States," he said. "There has been a lot of interest both at home and abroad."

Fallon said the government would prefer to float the state-owned company, a forerunner of which was set up by Henry VIII in 1516, on the stock market and grant postal workers 10% of the shares in the company. "Our preference is for an IPO, but if that's not possible we would look at alternatives [such] as sovereign wealth funds or other institutional investors."

He said the government would much prefer to keep Royal Mail British and "not delay any longer" giving staff a 10% stake in the business. But he said the Communication Workers Union's (CWU) strong objection to privatisation, despite the payout of an expected £1,500 to each of Royal Mail's 130,000 staff, meant the government had to plan other sale options.

Keeping Royal Mail in state hands was not an option, he said, and urged the CWU to end its campaign to keep the postal service government-owned. "We can't divert capital we need for schools and hospitals to Royal Mail – a very large business making substantial profits," Fallon said.

He said he was "surprised" by the CWU's "ideological objection to privatisation that would benefit all their membership [via] ownership of real stake and dividends". He added: "I would prefer the staff to have their stake now. Instead they [the union leaders] have organised an ideological ballot on the premise of privatisation."

He said a sale into foreign hands "would certainly be less popular with postal workers" and would "delay them getting the shares that parliament said they should get".

Billy Hayes, the general secretary of the CWU, said: "The government is taking the Royal out of Mail and selling out British interest. No wonder Ukip is on the rise." He said that the government was "rushing into a fire sale of the family silver on the cheap" and a sale or flotation would result in a "worse deal for customers, staff and thousands of small businesses dependent on the Royal Mail".

Hayes said the government could not "buy off" postal workers with the vague offer of an indeterminate value of shares in the privatised company. "That's not going to cut the mustard," he said. "Our members don't want £1,500 if it is going to result in depressed terms and conditions and another five streets on a delivery."

Fallon refused to state exactly how much of a stake postmen and women could expect from the privatisation, but said he would be "disappointed if individual posties weren't able to have an investment above [£1,500]".

He said the value of the postal workers' stake, which was enshrined in law two years ago, depended on how much the company was worth on flotation or sale. City analysts have put a £2-3bn valuation on the company, which would mean £1,500-£2,300 per worker.

"Crucially the value depends on market and investor appetite," he said. The government hopes to appoint leading bankers to run the sale by the end of May, and hopes to start the process by the autumn.

Chuka Umunna, the shadow business secretary, said: "Royal Mail is a treasured national institution. Going about making veiled threats about what you'll do if you don't get your way is no way to treat a much loved, hundreds-of-years-old institution – or its workers."

Fallon said it was "hard to be accused of rushing the sale by Labour" who tried to sell off Royal Mail under the previous government. "It is hardly a rush – successive governments have been trying [to privatise the postal service] for 28 years," he said.

Margaret Thatcher, who privatised British Gas, British Airways, British Telecom and dozens of other state-owned institutions in the 1980s, famously refused to countenance a sale of Royal Mail, saying that she was "not prepared to have the Queen's head privatised". John Major and Lord Mandelson also tried, and failed, to sell the service.

Potential private buyers include private equity funds, such as CVC Capital Partners, which was in the running during the previous attempted sale in 2009. TNT, the Dutch postal group, was also interested in the previous sale, but it is thought to be mainly interested in Royal Mail's highly profitable parcel arm GLS.

Other potential buyers are likely to include the sovereign wealth fund of Qatar, which has being up large chunks of prime UK assets including Harrods, 95% of the Shard and stakes in Camden market and Sainsbury's.

Royal Mail made an operating profit of £144m in the first half of its latest financial year, on sales of £4.4bn. That compares with operating profit of £12m on sales of £4.2bn a year earlier. Its 2012-2013 full-year results, due to be released within the next two weeks, are expected show a further increase in profits.

The government reiterated its pledge to maintain the universal service obligation to deliver mail six days a week to villages as well as cities at the same prices no matter how Royal Mail is sold.