The Government came under a hail of criticism last night over the bonus of almost £1 million for the boss of the largely state-owned Royal Bank of Scotland.

Labour leader Ed Miliband accused David Cameron of a "disgraceful failure of leadership" and unions branded the £963,000 award "utterly immoral", while Tory Mayor of London Boris Johnson said he was "bewildered" by the payout.

But Chancellor George Osborne said that the only alternatives would have been more expensive for the taxpayer. Ministers could have blocked the bonus only by tearing up the "arm's length" arrangements drawn up when RBS was saved from collapse in 2008 and taking over day-to-day operations at the bank, he said.

Speaking to broadcasters in the Swiss ski resort of Davos, where he is attending the World Economic Forum, the Chancellor said he recognised the "frustration" over bankers' pay.

But he added: "The alternatives 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 overruled the board, and I think that would have cost the taxpayer more as well."

The bonus deal, negotiated amid intense political pressure, was about 60 per cent lower than reports initially suggested. Stephen Hester, who has a salary of £1.2 million, could receive 3.6 million shares in the 83 per cent state-owned financial institution, which cannot be cashed in until 2014.

UK Financial Investments (UKFI), which oversees the Government's stake in RBS, said the figure reflected the "significant contribution" Mr Hester made towards rebuilding the bank in 2011.

While RBS's share price has halved and the company has shed thousands of jobs over the past year, Downing Street said "good progress" had been made towards achieving its objectives by slicing around £600 billion from an overblown balance sheet and increasing lending to business.

The Prime Minister's spokesman said it was "ultimately a matter for Stephen Hester" whether he chose to accept the bonus, after Liberal Democrat minister Jeremy Browne issued an outspoken appeal to the banker to turn it down.

Deputy Prime Minister Nick Clegg said he had "a lot of sympathy" for Mr Browne's argument, but insisted it was an "individual decision" for the banker.

But Lord Myners of Truro, who was a Labour minister at the Treasury at the time RBS was taken into public ownership, challenged Government claims that the contract ties UKFI's hands in bonus negotiations.

Lord Myners said: "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."