The cap on bankers' bonuses was introduced in the wake of the 2008 financial crisis.
It limits the annual pay-outs to twice a banker's salary after astronomical sums were commonplace in the early 2000s.
Mr Kwarteng is now said to be considering scrapping the cap as part of a wider post-Brexit overhaul of City regulations.
The intention is to make London a more attractive place for global banks – but unions and economists were among those criticising the timing of the proposal.
The TUC federation of trade unions said Mr Kwarteng should focus on raising everyone’s wages rather than “boosting bumper bonuses for those at the top”.
Chancellor Kwasi Kwarteng leaving No.10
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Liz Truss attending her first PMQs as Prime Minister
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Liz Truss’s Chancellor has promised a growth-focused shake-up of the economy and told City bosses last week: “We need to be decisive and do things differently.”
But considering allowing bankers’ bonuses to soar as millions feel the strain of the cost-of-living crisis is proving controversial.
TUC general secretary Frances O’Grady said: “Bonuses in the City are already at a record high.
“While City executives rake it in, millions are struggling to keep their heads above water.
“Working people are being walloped by soaring prices after the longest and harshest wage squeeze in modern history.
“The Chancellor’s number one priority should be getting wages rising for everyone – not boosting bumper bonuses for those at the top.”
City bosses have been critical of the cap introduced by European Union legislation, but supporters say unfettered bonuses aided the excessive risk-taking that led to the financial crash.
Luke Hildyard, the executive director of the High Pay Centre think tank, said removing the cap would be an “ideological measure” that favours the rich.
He added: “The bonus cap has probably helped to contain bankers’ pay awards but they’ve still reached record highs this year while the rest of the country has undergone an epic cost-of-living crisis and profound economic hardship.
“We know that bonuses in the financial services sector have helped the richest 1% of the population to capture an increasing share of total UK incomes.
“Removing the cap would be a pro-rich ideological measure that sends a depressing message about who policymakers listen to and think about when making economic policy.”
Gary Smith, the general secretary of the GMB union, said: “Apparently frontline workers asking for a pay rise risks increasing inflation, while allowing fat cat bankers to trouser monstrous bonuses ‘attracts talent’ and ‘boosts the city’.
“It’s rank hypocrisy. There is no doubt whose side this Government is on."