The chief executive of the taxpayer-funded Royal Bank of Scotland (RBS) is facing mounting pressure to follow the bank's chairman and waive his bonus of almost £1 million.

News of a double bonus scheme that could greatly inflate Stephen Hester's £1.2 million annual salary to a possible £8 million over the coming years has fuelled calls for him to forgo a shares bonus worth £963,000.

Two Sunday newspapers unearthed evidence of a "long-term" bonus package which would substantially increase the RBS boss's pay package. The Independent on Sunday claimed it would rise by £3.3m, while the Sunday Times believes it could rise by as much as £8m.

But speaking on Sunday morning, work and pensions secretary Iain Duncan Smith reiterated David Cameron's view that the government would not directly intervene in the row.

"The government made it clear to the board they should take into consideration the views of the public," he said.

"This is in shares. They're not exercisable until 2014 anyway, and they can be clawed back. The second thing is, I've heard a lot of talk about what the government can and can't do. The board takes the decision on this, the only option would be to get rid of the board. Imagine what would happen if we did that to the banking sector, there'd be chaos.

"We need to get this bank to a point where we can actually sell it."

Meanwhile a new poll published on Sunday showed that few people believed top bosses should earn more than £1 million a year. A survey of over 2,000 adults by the High Pay Centre research group found that two-thirds wanted to rein in "crony capitalism" and almost as many did not believe that top pay rates were set in an open and transparent way.

Just 7% of those questioned supported £1 million salaries for chief executives of firms in the Ftse 100, while only 1% said senior bosses were worth the £4 million currently earned by those at the top end of business.

Two out of three people agreed there should be a worker representative on company remuneration committees, a move which the Government ruled out earlier this week in its announcement on tackling excessive pay.

Deborah Hargreaves, director of the High Pay Centre, said: "Top executive pay and the behaviour of business are issues at the heart of the current public debate about how we rebuild our economy.

"Our polling shows the public do not believe executives, even of the biggest companies, should be awarded multimillion-pound pay packages. It is time for boardrooms to wake up to what is fair and act now to rebuild public trust."

A stark contrast came to light yesterday when it was announced that RBS's chairman Sir Philip Hampton had decided to decline a £1.4 million payout.

Sir Philip, chairman of RBS since 2009, had been on course to claim 5.17 million shares in the financial institution in February, but it is thought he told the bank's remuneration committee it would "not be appropriate" for him to take the shares to which he is entitled.

He was given the scheme when he was appointed at the 83% state-owned bank as part of a three-year long-term incentive deal.

An RBS spokesman said: "Sir Philip Hampton will not receive the 5.17 million shares he was awarded in 2009 when he joined RBS."

Mr Hester is entitled to both short-term bonuses and long-term incentive bonuses based on factors such as performance and meeting targets.

The £963,000 he was awarded last week was a short-term bonus equalling 3.6 million shares, relating to the 2011 calendar year.

Short term bonuses are capped at 200% of his annual salary, so his last payout was not as large as it could have potentially been. The long term scheme is based on the previous three years, so Mr Hester is approaching the point at which it can come into effect.

It is thought the long term bonus could potentially reach £8 million, but it is unlikely that maximum target will be met.

Prime Minister David Cameron sidestepped calls on Saturday to personally block Mr Hester's award, saying: "It is a matter for him."

Speaking at Chequers, Mr Cameron told journalists: "It's obviously his decision. My decision is to make sure the team at RBS get on with the job of turning the bank round and we made our views very clear on the bonus and that's why it was cut in half compared to last year."

He warned installing a new top team at the failed bank could be even "more expensive" than it is now.

"I think we need to get the facts straight," he said.

"The fact is Stephen Hester was brought in by the last government, a contract signed by the last government to turn round RBS - a bank that had got itself into a complete mess.

"The Government has made its views known and that is why his bonus was cut in half compared to last year.

"But we do have to bear in mind that the alternatives to what's happening now could be even more expensive if you had a whole new team coming into RBS."

Although some of RBS' shareholders agree with the PM, his position is at odds with that of Boris Johnson, who believes it should be within the control of ministers to determine the bonuses at the largely state-owned bank.

Labour leader Ed Miliband led calls for the Prime Minister to take action, insisting he had "another chance" to change his mind at the RBS Annual General Meeting.

He said: "Freezing the pay of a nurse or hospital porter, while allowing a publicly owned bank to pay million-pound bonuses is the last nail in the coffin of this Prime Minister's claim that we're all in it together.

"Having spent weeks boasting he would block bonuses, David Cameron refuses to even publicly explain why he has changed his mind.

"My message to him is - you've got another chance.

"At the AGM in April the Government as the majority shareholder in RBS will have to decide how to vote on the bonus. They should vote it down."