Shareholders in the oil giant are concerned that rises for Mr Dudley and other executives come despite job cuts and falling profits, reports The BBC.
Those who have spoken out include Aberdeen Asset Management and Royal London Asset Management.
But BP said the firm’s performance beat most measures that determine pay.
The pay rise for Mr Dudley takes his salary package to £14m.
Shareholder group Sharesoc branded the pay deal “simply too high”, while Glass Lewis, ShareSoc, Pirc and Institutional Shareholder Services have also expressed their opposition.
Ashley Hamilton Claxton, corporate governance manager at Royal London, told the BBC: “The executives received the maximum bonuses possible in a year when [BP] made a record loss, and to us that just does not translate into very good decision-making by the board.
“We think it sends the wrong message. It shows that the board is out of touch.”
Meanwhile, the Institute of Directors warned on Wednesday that the pay increase risked sending “the wrong message to other companies”.
IoD director-general Simon Walker said the “pay package will seem unjustified to many shareholders, considering the performance of the company over the past 12 months”. Last year, BP made a £3.6bn loss and announced that thousands more jobs would be cut.
The vote on BP’s remuneration report is “advisory”, so even a vote against would not strictly require any change of tack from the company.
However, Ms Hamilton Claxton told the BBC’s Today programme that 20%-25% of shareholders might vote down the pay deal, which would force BP to “think long and hard about their decision”.
BP’s pay policy is subject to a binding shareholder vote every three years.
