Pressure was mounting on David Cameron on Saturday to rein in pay at the Royal Bank of Scotland after it emerged that more top members of staff could be in line for bumper bonuses in the coming weeks.

Amid widespread public anger over lavish rewards at the taxpayer-backed bank, the Labour leader, Ed Miliband, is calling on Cameron to appear before the House of Commons to justify the bonus of almost £1m awarded to RBS's chief executive, Stephen Hester.

The row has also divided the coalition. Lib Dem peer Lord Oakeshott told the Observer: "Every single Lib Dem I know is against Hester getting a penny of bonus."

The political row is likely to intensify over the next few weeks as the RBS board decides whether to pay out bonuses to other senior staff members. Finance director Bruce van Saun would be handed 2.25m shares, worth about £600,500 at the current price, if his 2011 bonus is handled in the same way as that of Hester – who is getting 60% of his entitlement for 2011.

Other senior staff who do not sit on the board are also expecting bonuses for 2011 – and in addition, waiting to learn how many shares will be paid out from awards they received in 2009. John Hourican, head of RBS's investment bank, could be handed shares worth £4m in April. The precise value will depend on the share price and whether performance criteria have been met. Four bankers were allotted shares in 2009 that will be due after the bank's results next month. One was awarded 6m shares (worth about £1.6m at the current price) and the other three about 1.8m each (£500,000), though the actual number of shares the bankers receive will be based on performance targets.

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

Labour is calling on UK Financial Investments, the body that manages the government's shareholding in RBS, to register a protest about Hester's bonus at the bank's forthcoming annual general meeting.

The prime minister sought to defuse the issue on Saturday, as sources claimed that the business secretary Vince Cable was furious about the government's failure to block it.

Speaking from his Chequers country retreat, Cameron said: "The government has made its views known and that's why his bonus was cut in half compared with 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."

Sir Philip Hampton, the RBS chairman, was awarded 5.2m shares when he joined in 2009, which he was due to receive next month, subject to performance criteria. It is thought that those were not met, although Hampton had already decided to ask the board not to consider releasing the award to him.

The fresh controversy at the taxpayer-backed bank erupted as a new survey reveals widespread public scepticism about whether Britain's bosses are worth their bumper pay packages. Just 7% of more than 2,000 people questioned by pollsters ICM for the High Pay Centre, an independent inquiry set up by the Compass thinktank, thought that top executives should earn more than £1m, including bonuses and pension contributions. Only 1% thought they should earn more than £4m, the average level for FTSE100 bosses.

Deborah Hargreaves, the centre's chair, said: "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."

The timing of the RBS row is particularly unfortunate for David Cameron, who made a high-profile speech earlier this month calling for "responsible capitalism", and is planning to introduce rules to increase shareholders' control over boardroom pay.