The government's desperation to sell Royal Mail cost taxpayers £750m in a single day, the National Audit Office has said in a scathing report into the privatisation of the 500-year-old national institution.

The public spending watchdog says the business secretary Vince Cable ploughed ahead with plans to float Royal Mail at a maximum price of 330p-a-share despite repeated warnings from City experts that the government had vastly undervalued the company.

The audit office said in a report today that Cable chose not to heed the warnings and increase the flotation price from the 260-330p range because of fears it could put off institutional investors and jeopardise the flotation as postal workers were preparing for nationwide strike action.

The watchdog said the business department's keen desire to achieve a successful sale of Royal Mail within this parliament "resulted in the shares being priced at a level substantially below that at which they started trading".

Royal Mail's shares spiked 38% on their debut on the stock market on 11 October - the biggest one-day rise in a privatisation since British Airways in 1987 - as investors tried to buy up more than 23 times the number of shares available.

The audit office said the government could have made an additional £750m for taxpayers if it had priced the sale at the first day closing price of 455p rather than the maximum 330p starting price. Achieving an additional £750m from the sale could have covered the annual salaries of an additional 34,000 NHS nurses.

The early jump in the share price, dismissed by Cable as "froth and speculation" was followed by a continued rise to a peak of 618p in January. The shares closed at 563p yesterday, still 70% higher than the float price.

Amyas Morse, head of the audit office, said: "The department was very keen to achieve its objective of selling Royal Mail, and was successful in getting the company listed on the FTSE 100. Its approach, however, was marked by deep caution, the price of which was borne by the taxpayer."

Cable said: "Achieving the highest price possible at any cost and whatever the risk was never the aim of the sale. The report concludes there was a real risk of a failed sale attached to pushing the price too high. And a failed sale would have been the worst outcome for taxpayers and jeopardised the operation of Royal Mail."

The audit office said the government's pricing decision was largely influenced by Cable's desire for "long-term, blue chip" institutional investors to buy and hold large chunks of Royal Mail shares.

Despite overwhelming public demand for the shares (the public ordered enough to own the whole of the postal service but were cut down to just £750 per person), Cable allowed 16 long-term investors, mostly pension funds, priority access to the shares.

The audit office said this was part of the government's "expectation that they would form part of a stable long-term and supportive shareholder base".

At the time, Cable said: "We wanted to make sure that the company started its new life with a core of high quality investors who would be there in good times and bad, interested in Royal Mail and the universal service it provides for consumers over the long term."

However, the audit office said six of the 16 "priority investors" selected by Cable had sold all of their allocation within weeks of the float, at a substantial profit.

The watchdog said that by the end of January 2014 just 12% of the company's shares were held by the "priority investors".

A large proportion of their shares were gobbled up by hedge funds, which Cable has repeatedly attacked for being short term investors, describing them as "spivs and gamblers".

Within a fortnight of the float, a London hedge fund whose boss was memorably described as a "locust" by German politicians, bought up so many shares that it became Royal Mail's second-biggest investor after the government, which retained a 30% stake.

The Children's Investment Fund, which is run by billionaire Chris Hohn, bought up 5.8% of the shares. It has since cut its stake down below 5%.

The audit office also criticised the government for relying too heavily on its advisers, predominately the investment bank Lazard. The watchdog said the government gave Lazard an incentive "solely to complete a transaction" – not to achieve the maximum value for taxpayers. "The taxpayer interest was not clearly prioritised within the structure of the independent adviser's role," the audit office said in its report. And it revealed that the government asked its advisers if it should increase the offer price in the days before the float.

The department's banking advisers said the top of the price range could be increased by 20p to 350p - which would have made an extra £120m for taxpayers. However, Lazards and the banks advised against increasing the price for fear it could have put off investors. This was despite some of the banking syndicate's analysts valuing the shares as high as 510p, with no one reckoning they were worth less than 300p. Lazards advised selling the shares at between 212-262p.

Lazard was paid £1.5m for its advice. The government spent a total of £12.7m on fees to bankers, including UBS, Goldman Sachs, Barclays and Merrill Lynch, accountants, lawyers and PR advisers.

Margaret Hodge, chair of the public accounts committee, said the department for business made a "critical error by incentivising its private advisers to sell the shares on time at the expense of price".

She said the 70% rise in Royal Mail's share price since flotation shows that the department "had no clue what it was doing". Hodge said she was looking forward to "discussing this second class performance" when the department gives evidence to the committee in May.

Chuka Umunna, the shadow business secretary, said the audit office's report was a "damning verdict on the Tory-led government's botched Royal Mail fire sale, leaving the taxpayer disgracefully short changed by hundreds of millions of pounds".

Billy Hayes, general secretary of the Communication Workers Union that represents postmen and women, said the report "finds the government guilty"of overseeing a "get rich quick" scheme which offered no value to taxpayers.

Unite national officer Brian Scott said: "This report is startling proof that the government sold off the country's family silver on the cheap."