Image: BP Group
Tim Bush, head of governance at one of the shareholders planning to vote against the move, Pirc, told the BBC that the "pay model is broken".
"There is a major problem in the way chief executives are recruited and paid," he said.
BP's senior management pay is calculated by a formula agreed by 96% of shareholders in 2014. One shareholder said they blame the board, rather than Mr Dudley himself.
The Institute of Directors, which itself admitted doesn't often intervene in such matters, warned BP that governance guidelines suggest that pay should be linked to performance.
Simon Walker, director general of the Institute of Directors, said: "How the board of BP reacts to this rebellion will determine the future of corporate governance in the UK. The shareholders have spoken, and BP cannot shrug of this significant expression of disapproval with the CEO’s pay package. British boards are now in the last chance saloon, if the will of shareholders in cases like this is ignored, it will only be a matter of time before the Government introduces tougher regulations on executive pay."
He also said: “BP is not a badly run company, and its current woes are common to other firms in the sector. Nevertheless, the UK Corporate Governance Code is clear that pay should be tightly linked to performance and that targets should be stretching and rigorously applied. Should the pay package be approved, it could send the wrong message to investors and other boards."