More than 700,000 people have applied for shares in Royal Mail, the government has revealed, reviving privatisation fever last seen in the 1980s and intensifying fears that the postal service is being sold too cheaply.

Vince Cable, the business secretary, said the public had placed orders for more than seven times the number of shares available to them. Small investors could have bought the entire company if 70% of the shares on sale had not been reserved for City investors and pension funds.

"We haven't yet got the final figures but my very rough estimate is that we've had about 700,000 applications and it's about seven times oversubscribed," Cable told MPs. The huge demand for the shares means that applications are bound to be scaled back.

Those applying for the minimum £750 of shares may be the only ones to get what they have applied for while those who applied for shares worth thousands are expected to get just a fraction of what they had wanted.

The frenzy for the shares – fuelled by expectations of an immediate paper profit of 20% to 30% when trading begins on Friday – is more intense than demand for British Gas or British Telecom was at the height of the privatisation drive in the 1980s and 1990s.

The public put in orders for just four times the number of British Gas shares available in its 1986 privatisation despite its multimillion-pound "Tell Sid" advertising campaign. The privatisation of BT in 1984 was 3.2 times oversubscribed. More than 4 million people applied for British Gas shares, while 2 million applied for BT shares.

Cable said he was confident the shares had been "priced in the right place" despite claims from City analysts that the government undervalued the company by more than £1bn.

The business secretary said the claim by stockbroker Panmure Gordon that Royal Mail is worth £4.5bn compared with the government's maximum valuation of £3.3bn was "way outside the estimates of most of the equity analysts".

The shares will almost certainly be priced at 330p and will make their debut on the stock market on Friday. Stockbrokers predict the shares could rise to between 385p and 405p on the first day. A rise to 400p would mean investors would make an immediate 21% paper return.

If the shares rise by 20% on Friday, £750 of shares will be worth £900 by the end of the afternoon. It also means the government will have lost out on collecting an extra £400m for taxpayers on top of the £2bn it will collect from selling the 60% stake of Royal Mail. A further 10% is being given to the company's 150,000 employees – each will collect shares worth about £2,200.

Cable said people should ignore the immediate "froth" of the expected share price jump on Friday and concentrate on Royal Mail's secure long-term future on the public market.

Ian Murray, the shadow minister for postal affairs, said: "I don't think taxpayers losing millions is froth."

Selling Royal Mail, which traces its roots back to a forerunner founded by Henry VIII in 1513, has been on the political agenda for decades. Margaret Thatcher, the pioneer of privatisation in the 1980s drew the line at Royal Mail, saying famously that she was "not prepared to have the Queen's head privatised". But both the Tories' Lord Heseltine and Labour's Lord Mandelson tried, and failed, to sell it.

The sale now comes despite massive opposition from staff, 96% of whom are adamantly against the sell-off despite picking up free shares. Royal Mail's army of 150,000 workers are currently balloting on holding days of paralysing strike action in the runup to Christmas.

Because the shares are so oversubscribed orders from the public as well as from banks are likely to be significantly scaled back. The government is likely to honour all public orders for the minimum £750 of shares, but larger orders will be severely cut back. Michael Fallon, the business minister, has said he is committed to making sure small investors "get their fair share" of Royal Mail shares.

The government has only committed to granting 30% of the £2bn of shares available to the public but the government refused to say whether a greater proportion of the shares on offer will be transferred to the public rather than institutional investors.

The 30% earmarked for the public would work out at only £857 each if split evenly between the 700,000 applicants. A government spokesman said the exact details of how the shares will be distributed will not be announced until Friday morning.

On top of the massive public demand, hedge funds and other institutional investors are understood to have placed orders for more than £30bn of Royal Mail shares.

Cable said institutional demand was so strong that the government would be able to block shares from going to "spivs and speculators" in favour of "responsible long-term institutional investors".

"We are in a position to ensure we do get the right type of investor community – pension funds insurance companies that hold the savings of millions of people," he said. "That's the type of community we want."

Cable said demand from institutional investors at the maximum 330p is so strong that hedge funds and other speculators "in it to make a killing" are unlikely to end up with any shares in the flotation. "The aim is to place the shares with long-term investors, we are absolutely confident that will happen."