The furore over the sale of Royal Mail has erupted again after it was revealed that investment banks had estimated the company's value at up to £1.5bn more than its flotation price.

Figures released by the business department on Friday showed that of 21 City advisers that supplied early valuations in May, the average ranged from £4bn to £4.8bn. The government sold 60% of its stake in October in a privatisation that valued Royal Mail at £3.3bn.

Royal Mail's shares jumped by more than a third on their first day of trading, raising concerns that the sell-off was too cheap. They have risen further since to 588p – 78% higher than the flotation price.

Chuka Umunna, Labour's shadow business secretary, who obtained the figures in a freedom of information request said: "David Cameron has serious questions to answer about why his government sold off Royal Mail on the cheap. We now know that the vast majority of banks that provided valuations to the government expected the company to be worth more than the government sold it for."

Business minister Michael Fallon, who oversaw the privatisation, said: "The banks who made these early valuations have admitted they cannot be compared with those reached at the end of any sale process. We carried out a successful sale that secured almost £2bn for the taxpayer and long-term investors in Royal Mail.

"We still own a 30% stake in the company and the subsequent rise in the trading price of shares in Royal Mail ensures that taxpayers continue to benefit from any strengthening in the share price."

The investment banks that advised on the sale, Goldman Sachs and UBS, told MPs on the business select committee in October that the flotation took place when financial markets were jittery and with the threat of a nationwide strike looming over Royal Mail.

They considered increasing the price by 20p a share but recommended against it when big fund managers said they would be reluctant to accept the higher price, they said. In the circumstances the sale was a success, they argued.

Vince Cable, the business secretary, told MPs before the flotation that the shares would need time to settle down and to lose their post-privatisation "froth".

Nick Clegg tried to defend Cable, his fellow Liberal Democrat minister.

On his regular phone-in on London's LBC radio station, the deputy prime minister said: "Vince is not a sort of share price expert, he is the secretary of state who is responsible for this … He took advice from people who gave him a range, independently, of what … the fair share price should be. And actually, he set the share price at the very highest point in the range that he was given."

The CWU union opposed Royal Mail's privatisation but has since agreed a three-year pay deal and groundbreaking five-year agreement over terms and conditions.

Billy Hayes, the CWU general secretary, said: "These latest figures come as no surprise and show the government's main concern in selling off Royal Mail was to get a good deal for the rich resulting in a bad deal for the rest of us.

"Vince Cable had the opportunity to make the Treasury a significant sum but instead he flogged off this cherished national institution at a bargain basement price. Vince Cable previously dismissed these claims as 'froth' but now it is clear to see the government's priorities lie in topping up investors' profits at the expense of consumers and taxpayers."

On Wednesday, Cameron refused to say the government got the best deal for the taxpayer. "The government did a good job to get private sector capital into Royal Mail. Frankly, that is something that has evaded Governments of all colours and all persuasions for decades," he said during prime minister's questions in the Commons.

The lowest valuation received by the government said Royal Mail could be worth between £2.8bn and £3.2bn. The highest attached a value of between £6.9bn and £8.7bn. JP Morgan told MPs in October that its early stage valuation was between £6.8bn and £8.5bn.