Angry investors are demanding that Shell pays back millions of pounds of bonuses set to be awarded to the oil giant's most senior executives - payments in defiance of a vote at the company's annual meeting last week.

Over the weekend, several large shareholders vowed that their increasingly militant campaign would continue, and stepped up the pressure by demanding the resignation of the chairman of Shell's remuneration committee, Sir Peter Job, who has been at the centre of the row over remuneration.

Shell chief executive Jeroen van der Veer is on eight-figure remuneration, with a £1 million ($2.57 million) bonus on top of his £9 million salary.

The fury about Shell came as the Royal Bank of Scotland, now majority owned by the UK taxpayer, revealed that four senior staff are eligible for share windfalls of £5 million, including a package of £2.4 million for Ellen Alemany, the head of the bank's US business. Alan Dickinson and Chris Sullivan, heads of corporate banking division, are also in line for large bonuses.

RBS, bruised by the high-profile fights over former chief executive Sir Fred Goodwin's £700,000 per year pension, emphasised that the rewards were subject to stringent targets.

Such targets were, according to major shareholders, missed at Shell, where more than 59 per cent of shareholders voted against the remuneration report at the transnational's AGM last week. This is itself a highly unusual event, but the company's management immediately raised the stakes by responding that it would merely take the vote into account.

That is not good enough for some. Abigail Herron, speaking for Co-operative Asset Management, commented: "Legally, Shell can do what it wants on this one, but on moral grounds, the bonuses should be paid back to shareholders."

Alan MacDougall, managing director of investor activist group Piric, added: "Jobs was chairman of the committee that decided to use its discretion to award these bonuses, so he must carry the can ... Shell is another example of how executive pay and performance are so often misaligned."

A number of fund managers said Sir Peter should quit.

Shell said after last week's AGM vote that it would "reflect carefully" on the result and had "introduced additional performance measures for future awards". The recession has embittered a long-running debate on executive pay, especially at larger corporates and those in financial services.