The government has confirmed it will sell off Royal Mail in "the coming weeks" in the most contentious privatisation since the sale of the railways two decades ago.

Vince Cable, the business secretary, on Thursday formally fired the starting gun on the £3bn sale by filing a formal "intention to float" on the stock exchange within six weeks. At least half of the company will be floated and the size will be increased if there is sufficient demand from investors.

The sell-off of the 497-year-old postal service is forcefully opposed by the union, who are planning strike action timed to coincide with the sale.

Billy Hayes, deputy general secretary of the Communication Workers Union (CWU), said the sale will lead to worse terms and conditions for staff while "people in the City and the board make a killing".

"This isn't about what's best for Royal Mail, it's about the vested interests of government ministers' mates in the City," he said. "It would be bad for customers, bad for staff and bad for the industry. Privatisation would put jobs and services at risk and lead to higher prices for customers."

Cable said privatisation was necessary to "secure a healthy future for the company". The government says Royal Mail must be sold so that it can borrow private money and not compete against schools and hospitals for public funds.

The union opposes the sale despite the government promising 150,000 postal staff a 10% stake in the company – worth up to £2,000 each – for free. The government also promised staff they will share a further £13.3m (about £90 each) in dividend payments in the first year, and more in following years.

Hayes said 96% of Royal Mail staff oppose the sell-off, which "not even Thatcher dared do".

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 she was "not prepared to have the Queen's head privatised".

Lord Heseltine and Lord Mandelson both subsequently tried but failed to sell the company, in the face of intense opposition from MPs. The sale of Royal Mail was approved by parliament in the 2011 Postal Services Act.

The CWU plans to disrupt the sale process by holding a strike ballot on 20 September, which could lead to a nationwide strike by 10 October. It would be the first nationwide postal strike since 2009. The union is also pushing for a better pay deal, after rejecting a 8.6% pay rise over three years.

Moya Greene, Royal Mail's chief executive, met union members on Thursday to implore them not to strike. Greene was booed as she took to the stage, according to a CWU representative who tweeted from the meeting in Birmingham.

The public will be able to buy shares via stockbrokers or directly from the government via postal or online applications. Members of the public will have to buy at least £750 worth of stock, while Royal Mail employees will have preferential access to more shares if they spend at least £500.

Chuka Umunna, the shadow business secretary, attacked the government for "pushing ahead with this politically motivated fire sale of Royal Mail to fill the hole left by George Osborne's failed plan".

Simon Walker, director general of the Institute of Directors, said the government is "absolutely right" to privatise the world's oldest postal service.

"Royal Mail employees should see this as a great opportunity, not only to own a stake in their company, but also to give it the best chance to succeed in a competitive delivery market," he said. "The unions must acknowledge that strike action is not in the best interests of the business or their members."

Mario Dunn, campaign director of Save Our Royal Mail, said: "This might be good news for the bankers but it is bad news for Royal Mail customers.

"The elderly, people in rural areas and small businesses will be particularly hard hit by the inevitable price rises and service reductions that will follow this privatisation.

"Royal Mail is a successful public sector enterprise. This is an unnecessary and ultimately political privatisation."

The government promised that sale will not affect Royal Mail's universal service obligation to delivery to 29m addresses Monday to Saturday for the same price. However, the union warns that private owners will campaign to end the expensive obligation.

The privatisation of Royal Mail does not affect the Post Office, which was split into a separate company in April last year.

Greene said: "Our strategy is delivering a revitalised company, with a unique UK, multi-use network through which we are proud to deliver the universal postal service for all UK citizens.

"This network and our strong brand, coupled with the high service quality delivered by our people enable us to take full advantage of the growth in UK e-commerce to further enhance our pre-eminent parcels business. Combining this UK presence with our pan-European parcels business GLS, should result in a financial profile that combines revenue growth and margin progression to underpin strong cash flow generation."

Royal Mail traces its roots to a forerunner set up by Henry VIII in 1516.