The flag was the centrepiece of an agreement-signing ceremony
The government has said it regrets displaying the Union flag upside down at the signing of a trade agreement.
A plastic flag was flown incorrectly for a ceremony involving Gordon Brown, Chinese premier Wen Jiabao and Trade Secretary Lord Mandelson.
The Flag Institute said it was "concerned" about the mistake and Tory MP Andrew Rosindell called it "an unbelievable flaw in protocol".
BBC News website readers got in touch to point out the error.
The Union flag - more commonly described as the Union Jack - has been in use since the Act of Union between Great Britain and Ireland came into force in 1801.
There is a specific way of hanging it, with the thick white parts of the diagonal cross nearest the flagpole being placed above the thinner white parts.
But, at the treaty-signing ceremony in Downing Street on Monday, a flag was displayed upside down.
Close-up view of the flag as displayed by Downing Street
Mike Kearsley, director general of the Flag Institute, said: "My first reaction is 'here we go again'.
"One part of me is concerned that we don't recognise and understand our own flag but another part of me is amused that it's a terribly British thing to do.
"You would think people in Downing Street would recognise it because they see the flag so often. Many places in government these days have people working from overseas and maybe they don't understand.
The flag as it should be displayed
"If we had flown the Chinese flag upside down it could have been quite a diplomatic problem."
Mr Kearsley added: "I'm surprised that people of the calibre of Mandelson and the prime minister could allow such as mistake.
"They were just little plastic flags on wooden sticks, which you could easily take off and put back the right way up.
"In some parts of Europe you will see four flags flying from public buildings - the national, EU, district and town flags. They seem to get it right. So should we."
The term Union Jack specifically refers to the flag flown at the front of Royal Navy ships when in port.
But it has become synonymous with the Union flag, with many experts now regarding the terms as interchangeable.
Mr Kearsley said: "Having the flag upside down historically was a sign of distress. You might have put it up on a fort to warn those in the know - other British forces - that there was trouble from the enemy.
"Forces from other nations wouldn't have noticed. It was like a sort of code."
Mr Rosindell, MP for Romford and chairman of the Commons all-party flag group, said: "It's an unbelievable flaw in protocol by Number 10.
"You would think they would know which way the flag was flown. Whoever is responsible for this should know better."
In a statement, Downing Street said: "It is regrettable that, on this occasion, the Union flag was not displayed correctly.
"We have looked into how this happened and have taken steps to ensure it is correctly displayed at all times in the future."