EU diplomats and the European Parliament agreed new rules last week that would prevent bankers from receiving bonuses bigger than their base salaries from next year. The bonus cap can rise to twice the size of the salary if shareholders agree.
Britain's powerful financial sector professionals fear the rules will put London at a disadvantage and provoke an exodus of major banks and staff to rival financial centres.
Osborne has argued against the limits and will repeat those objections at an EU ministers' meeting in Brussels. Few other countries, however, support his position, officials familiar with the discussions say, and since the measures only require a weighted majority of member states to become law, Britain has no veto.
An inability to fend off the reform, the first of its kind globally, also underscores Britain's waning influence in the EU and plays to a growing eurosceptic complaint that Brussels has too much say on domestic policy.
Late on Monday, France's finance minister Pierre Moscovici said the deal would not be renegotiated.
"Everyone must live with what is on the table," he told reporters after a meeting of eurozone finance ministers in Brussels. "I told George Osborne, when I was in London, these moral rules apply to everyone, even the City."
A spokesman for Prime Minister David Cameron had earlier said the British government had "real concerns" about the bonus cap plans and that it was discussing the situation with other member states. London Mayor Boris Johnson has dubbed the policy "moronic".
Perhaps the best that Osborne can hope for is that if other parts of the wider bank capital agreement are challenged, he could push back for a softening of pay curbs.
Britain could try to push to change the scope of the rules, which will apply to all EU bank staff globally regardless of where they are based, or propose extra flexibility on how bonuses are calculated.
British members of the European Parliament indicated that they had done as much as they could to accommodate Britain, with concessions such as allowing it flexibility on other elements of the new banking rules, which also cover capital requirements.
"The UK has got all of its other issues delivered on, such as flexibility to apply the retail ring fence for banks and many other issues to help the wider economy," Vicky Ford, a British MEP who played a role in negotiations, told Reuters. "But we can't have everything."
Ford said the bonus rules had already been changed significantly during negotiations.
The new rules will not apply to the majority of bank staff, who on average earn bonuses of up to 30% of salary, but target senior management and so-called "risk takers", such as traders, whose bonuses can be many times their base salary.
Analysts estimate the law will initially affect around 300 to 500 people in each large bank, or around 5,000 people in London all told.