Banks advising the government on the controversial sell-off of Royal Mail were allocated millions of shares that have shown a profit of about £29m since its flotation. The gains come on top of the near £17m handed over to the banks in fees for their advice on the float.

Ministers have revealed that City advisers helping with the flotation were given the opportunity to buy 13m shares in Royal Mail as investors rushed to buy into the new private company.

Since then, the government has been criticised for potentially short-changing the taxpayer by selling the shares at 330p, when they closed on Friday at a new record of 555p, valuing the company at £5.55bn – 67% up in a fortnight.

Vince Cable, the business secretary, has defended the price of the sell-off, saying value for money is "about more than just the level of proceeds received on day one".

A spokesman for the Department of Business said the government's advisers, including Goldman Sachs, UBS and other junior advisers, were not given preferential treatment when shares were allocated and some did not get any at all.

He refused to say how many shares were offered to each adviser. The spokesman stressed that it is "standard practice", saying there was no possibility of a conflict of interest because of "Chinese walls" between different banking divisions.

However, Adrian Bailey, the chairman of the House of Commons business committee and a Labour MP, late Friday raised questions about the process, saying he plans to grill ministers about how many shares were offered to each bank, their level of fees and their role in the valuation of the company.

"These are questions that I will ask on November 20th," he said. "When you look at the balance between the retail and the institutional percentage of shares allocated, and the potential conflict of interest from the advisers, I think there are grounds for looking at the whole way privatisations are carried out in future. Unfortunately the government at the moment seems completely blind to that and the perception it creates".

The shares were allocated to the banking advisers separately from the £16.9m of fees due to be paid for their role in the flotation, and may have been sold or added to at any point since the flotation date.

Their allocation emerged after Labour peer Lord Donoughue asked the government how many shares were sold to the banking advisers who advised on the price of the flotation.

Lord Popat, a Conservative whip, said no employee working on the transaction or investment bank division was allocated shares but "other divisions of our banking advisers, separated from the investment banking divisions by the information barriers, were allocated 13m shares".

A senior banking source strongly denied any of the banks would directly profit from the being allocated shares, saying they would have been bought to help make money on behalf of clients in the asset management divisions. He said there were strict Chinese walls at the banks that mean those advising on the deals would not even ever have met those buying shares on behalf of clients.

Goldman Sachs and UBS declined to comment.

The news comes amid reports that JP Morgan put a possible top-of-the-range valuation on Royal Mail at £10bn – more than three times the £3.3bn that it was eventually sold for by the government.

Chuka Umunna, the shadow business secretary, said there were now a "wide range of questions being asked about the government's Royal Mail fire sale which Ministers need to answer".

"While Vince Cable has claimed that guaranteeing taxpayer value was 'central' to his strategy, doubts are emerging on the process ministers put in place. We know that Vince Cable considered, and rejected, the option of getting a better deal for the taxpayer," he said.

"At a time when the public are seeing services cut back and their living standards squeezed, they will not forgive ministers if they are left short changed."