|The Asian Infrastructure Investment Bank agreement was signed in October |
by 21 countries, including China
The UK is the first big Western economy to apply for membership of the Asian Infrastructure Investment Bank (AIIB).
The US has raised questions over the bank's commitment to international standards on governance.
"There will be times when we take a different approach," a spokesperson for Prime Minister David Cameron said about the rare rebuke from the US.
The AIIB, which was created in October by 21 countries, led by China, will fund Asian energy, transport and infrastructure projects.
The UK insisted it would demand the bank adhere to strict banking and oversight procedures.
"We think that it's in the UK's national interest," said Mr Cameron's spokesperson.
Pippa Malmgren, a former economic advisor to US President George W Bush, told the BBC that the public chastisement from the US indicates the move might have come as a surprise.
"It's not normal for the United States to be publicly scolding the British," she said, adding that the US's focus on domestic affairs at the moment could have led to the oversight.
|Chinese construction site|
In a statement announcing the UK's intention to join the bank, Mr Osborne said that joining the AIIB at the founding stage would create "an unrivaled opportunity for the UK and Asia to invest and grow together".
The hope is that investment in the bank will give British companies an opportunity to invest in the world's fastest growing markets.
But the US sees the Chinese effort as a ploy to dilute US control of the banking system, and has persuaded regional allies such as Australia, South Korea and Japan to stay out of the bank.
This is, indeed, another nail in the coffin of American control of the world monetary system. I fully expect the AIIB to use the Chinese Yuan as its base currency thereby further weakening the American dollar as the base of the world economy. Having a major western economy sign-on to that is of very great concern to Americans, as it should be.
In response to the move, US National Security Council spokesman Patrick Ventrell said: "We believe any new multilateral institution should incorporate the high standards of the World Bank and the regional development banks."
"Based on many discussions, we have concerns about whether the AIIB will meet these high standards, particularly related to governance, and environmental and social safeguards," he added.
Analysis: Linda Yueh, BBC chief business correspondent
It's a tricky task to align oneself with both China and the US. The Americans are apparently unhappy with the UK, while China has welcomed the British application.
It may be a pragmatic move, but it's hard not to offend one side or another.
I suspect this will be the first of many decisions to be taken by countries such as the UK to position themselves between the new economic superpower and the existing one.
The trick will be to come away with economic advantage at minimal political cost. We'll find out if this one will pay off for the UK.
Some 21 nations came together last year to sign a memorandum for the bank's establishment, including Singapore, India and Thailand.
But in November last year, Australia's Prime Minister Tony Abbott offered lukewarm support to the AIIB and said its actions must be transparent.
US President Barack Obama, who met Mr Abbott on the sidelines of a Beijing summit last year, agreed the bank had to be transparent, accountable and truly multilateral.
"Those are the same rules by which the World Bank or IMF (International Monetary Fund) or Asian Development Bank or any other international institution needs to abide by," Mr Obama said at the time.
The Financial Times (FT) newspaper reported on Thursday that US officials had complained about the British move.
The report cited an unnamed senior US administration official as saying the British decision was taken after "virtually no consultation with the US".
"We are wary about a trend toward constant accommodation of China," the newspaper quoted the US official as saying.
However, in response to the UK announcement, World Bank president Jim Yong Kim told a news conference he supported the goals of the AIIB.
"From the perspective simply of the need for more infrastructure spending, there's no doubt that from our perspective, we welcome the entry of the Asian Infrastructure Investment Bank," he said.
The founding member countries of the AIIB have agreed the basic parameters that would determine the capital structure of the new bank would be relative gross domestic product.
Banking experts have estimated that, if taken at face value, this would give China a 67% shareholding in the new bank.
That's significantly different than the Asia Development Bank, which has a similar structure to the World Bank and has been in existence 1966. There, the majority stakes are controlled by Japan and the US.
|Tony Abbott poses with Chinese President Xi Jinping at the |
Apec summit banquet in Beijing - 10 November 2014
When asked if Britain would seek assurances before it signed on as a member that no one country would be able to unilaterally control the AIIB, economist David Kuo told the BBC that the UK "wouldn't have a great deal of say in the matter".
"He who pays the piper calls the tune," he said. "The UK could try and negotiate a power to veto projects but it is unlikely to get it," Mr Kuo, who is from investment advisers The Motley Fool, said.
The UK was caught between the US on the West and China in the East, he added.
"It hopes that it can exert force from within, rather than put pressure from the outside - but [the UK] is only one voice in a crowd of many."
With regard to the competition the AIIB would give the ADB or World Bank, Mr Kuo said there were plenty of infrastructure projects in Asia that needed funding.
"The existing sources of money can't do everything. So every little helps."