Taxpayers could lose out on more than £500m in the controversial privatisation of Royal Mail, Labour has warned.

Chuka Umunna, the shadow business secretary, attacked the government sell-off after a leading City analyst said the coalition had undervalued the 497-year-old postal service by more than £1bn. Nearly two-thirds of the company is being sold.

"It is truly shocking that taxpayers are set to lose out to the tune of half a billion pounds because the government has undervalued Royal Mail, as this [Panmure Gordon stockbrokers] report suggests," he said. "This analysis suggests that the true value of Royal Mail's shares is a third higher than the price the government is getting for its stake."

Umunna said taxpayers "will not forgive ministers if it turns out they have bungled the sale of this centuries-old institution and sold it on the cheap".

Gert Zonneveld, managing director of stockbroker Panmure Gordon, said he was convinced the government's official valuation of Royal Mail at £2.6bn-£3.3bn was a significant undervaluation.

Zonneveld believes Royal Mail is worth £3.7bn-£4.5bn, when compared with listed postal services in other countries. "I'm so convinced they [the government] got it wrong," Zonneveld said. "I think they're more than £1bn too low." Under Zonneveld's valuation, Royal Mail would join the FTSE100 list of Britain's biggest companies, which means tracker funds will be forced to buy the stock.

The Department for Business, which is running the sale, said: "The valuation will be determined by the book building process. The government has no intention to change the price."

The government's valuation was based on advice from investment banks Goldman Sachs and UBS after £21.7m in fees was paid to advisers.

Zonneveld predicted the controversial sell-off would be a raging success with the shares expected to soar by as much as 30% when they float on the stockmarket on 11 October. "I think this is going to be massively oversubscribed," he said. "Institutional investors who want £10m will increase their order to £50m because they know their orders will be scaled back."

Hedge funds are clamouring to buy shares, according to financial pundit David Buik. He tweeted: "I am hearing that a few hedge funds have subscribed for 100s of millions of shares in Royal Mail IPO!"

The massive demand means Royal Mail's stock will almost certainly be priced at the top end of the 260-330p-a-share price range, giving the company a market value of £3.3bn.

The strong demand means retail investors – the public – may not get all of the shares they have applied for. Retail investors will be allocated 30% of the shares on offer, with 70% going to banks and institutional investors. Orders for shares close on 8 October.

The government is selling up to 62% of Royal Mail, with 10% given away to the company's 150,000 staff. It is the biggest privatisation since John Major sold the railways in the 1990s.

Stockbroker ETX Capital said it was experiencing exceptional demand from retail investors and expected the shares to rise to 337-365p on the first day.

Broker Hargreaves Lansdown said it would stay open all weekend and until midnight on Tuesday to cope with the phenomenal public demand for the shares.

After the shares are listed on the stock exchange on 11 October, banks will be able to start trading. Retail investors will not be able to sell their shares until 15 October.

Umunna also raised concerns that the true value of Royal Mail's property assets, including prime sites in central London, have not been properly reflected in the government's valuation.

The Royal Mail sale prospectus lists three London sites as being surplus: the eight-acre site at Mount Pleasant in Islington, which Labour said could be sold for up to £1bn to luxury property developers; Nine Elms, valued at up to £500m; and a site at Paddington.

In its sale prospectus, Royal Mail estimated the value of its estate, which includes more than 2,000 properties across the country, at just £787m.

Royal Mail pointed out that sites similar to its London properties have attracted much lower valuations than those suggested by Labour.

A spokesman for the Department for Business said: "Royal Mail was clear about its intentions around property in the prospectus. The company disclosed details of its three major surplus sites currently undergoing pre-development work (including the Nine Elms site)." He added that most of Royal Mail's other properties were not available for redevelopment because they were vital to the company's operations.