Row erupts after prime minister claims that MPs had no choice but to agree to RBS head's bonus are challenged by Labour

David Cameron was under fire for failing to intervene to block a bonus of nearly £1m for Royal Bank of Scotland's chief executive, Stephen Hester, and for allegedly misleading parliament after he blamed Labour for negotiating a contract that prevented the government from intervening.

Boris Johnson, the mayor of London, speaking in Davos, piled the pressure on the prime minister by describing the bonus as "absolutely bewildering". Labour called on Cameron to appear before MPs to explain why he did nothing to block the bonus.

The row erupted on Friday morning when Lord Myners, the former Labour Treasury minister who negotiated the contracts with the new state-controlled banks, challenged the prime minister's claim that ministers had no choice but to agree to the Hester bonus, announced in the same week that the coalition announced proposals to hand shareholders more power to block pay deals.

"There is nothing in the employment contract of Stephen Hester or any director of Royal Bank of Scotland which binds the company or its remuneration committee to pay a mandatory bonus," Myners said. "All matters relating to bonuses are at the full discretion of the board of directors and the shareholders, including UKFI, who have elected them."

The prime minister, who indicated in recent weeks that Hester's bonus would be less than £1m, said the government had little room for manoeuvre because of the contract negotiated by the last government. The bonus is in shares, which rose to £981,000 last night – up from the £963,000 they were valued at by the bank in its announcement late on Thursday. The exact value will be determined in 2014 when he finally receives them while a three-year bonus he was handed in shares shortly after he joined in October 2008 – worth £6.4m – has now been deemed worthless by the bank.

Downing Street said that Hester's contract meant that he had to be considered for a bonus in "good faith". But the prime minister's spokesman admitted that a bonus was not mandatory and that the government, through UK Financial Investments, could have blocked it.

The spokesman said: "The contract says that he should be considered for bonus in good faith. That decision is taken by the board. Yes, shareholders have a role in that. UKFI, as the government's shareholder, takes a very active interest. But we are not the only shareholder in that company … The board is required to act in the interests of all its shareholders and the board takes this decision."

Downing Street admitted that Cameron was not relaxed by the bonus but said that Hester has reduced the RBS balance sheet by £0.5tn and has increased business lending in the last year.

But George Osborne, the chancellor, defended the bonus after a speech in Davos – but also distanced the government from the decision. "I would bet his bonus will be a lot less than the bonuses of other people running banks are going to get and half of what he got last year."

Bob Diamond, chief executive of Barclays – who was also in Davos, speaking at an event on "building trust" – refused to talk specifically about Hester's bonus, but commented: "If we don't celebrate reward for success we won't have an economy."

Diamond declined to comment on the scale of his own bonus, which could be in the region of £10m.

Osborne added: "The alternatives [to the Hester payout] would have been worse for the taxpayer. Either there would have been a much larger bonus, of the kind he would have got a few years ago. Or the British government would have had to take over complete ownership of RBS and over-ruled the board, and I think that would have cost the taxpayer more as well."

His comments did not appease critics. Ed Miliband, also in Davos, described it as a " disgraceful failure of leadership" by the prime minister. "He owns, through the British government, 83% of the Royal Bank of Scotland. He must now explain, not least to the British people, why he has allowed this to happen."

Labour sought to increase the pressure on the government by writing to the prime minister to ask him to set out to MPs why he said he was bound by a contract which is flexible.

Simon Danczuk, a Labour MP, said in the letter: " I trust you will want to come to the house to explain why you previously told the house that you did not have any such power, as well as to explain why your government has decided, in its role as the majority shareholder in RBS, to approve a bonus to Stephen Hester worth almost £1m."

The TUC's general secretary, Brendan Barber, also in Davos, described the decision to hand Hester a bonus as terrible. "The government might have been able to subcontract the decision [to UK Financial Investments] but they can't sidestep the responsibility." Already doubful that government plans to hand shareholders new powers to tackle high pay would be effective, Barber said: "The government through their stakes in the banks had the possibility of sending the signal. They've really bottled the decision".

It is not clear whether John Hourican, head of the RBS investment bank or Ellen Alemany, head of the US bank, will receive their bonuses this year.