Queen Elizabeth II was caught on camera describing some Chinese officials as "very rude" in a rare diplomatic gaffe by the British monarch over a visit that drummed up billions in Chinese investment.

Her comments, aired on Wednesday, came just hours after Prime Minister David Cameron on Tuesday also made inadvertently public remarks, referring to Afghanistan and Nigeria as "most corrupt".

Dressed in a pink coat and hat with white gloves, the queen could be heard during a garden party at Buckingham Palace on Tuesday making unguarded comments about a Chinese state visit last year.

Police commander Lucy D'Orsi was introduced to the queen as the woman who oversaw security for the state visit of President Xi Jinping and his wife in October, to which the monarch replied: "Oh, bad luck".

The queen went on to say to D'Orsi that members of the Chinese delegation "were very rude to the ambassador" and exclaimed: "Extraordinary!"

The BBC said that the queen's comments were blanked out on BBC World transmissions in China.

The British monarch never expresses overtly political views in public and is known for her discretion, never granting an interview in her 64-year reign.

Her husband Prince Philip on the other hand is notorious for his gaffes and off-colour jokes.

He told a group of British students during a visit to China in 1986 that they would become "slitty-eyed" if they remained in the country.

Prince Charles has had a famously fraught relationship with China because of his friendship with the Dalai Lama and has yet to make an official visit to the country's mainland.

He referred to Chinese leaders as "appalling old waxworks" in a private journal entry about the Hong Kong handover ceremony in 1997.

- 'Stressful' visit -

London and Beijing both hailed Xi's visit as a high watermark in Chinese-British relations at the time.

A clutch of contracts said by Cameron to be worth almost �40 billion (51 billion euros, $58 billion) were announced during the visit.

Chinese foreign ministry spokesman Lu Kang on Wednesday said the visit had been "very successful".

"Both sides have high level recognition of that," he said.

Foreign minister Philip Hammond, however, was quoted by British media as saying that the visit had been "a bit stressful".

Buckingham Palace said it would not comment on the queen's private conversations.

Rana Mitter, director of Oxford University's China Centre, said the comments were unlikely to hamper ties and "a significant pushback" from Britain on security for Xi's visit could have been expected.

"I think the Chinese are extremely pragmatic on these sorts of things. There is a perception that the UK is an important enough trading and political partners that this sort of incident isn't going to get in the way," he said.

"I suspect that Chinese officials are far more concerned about the prospect of Britain leaving the European Union than they are about the overheard comments of high-level figures," he said.

On Tuesday, Cameron was overheard at another Buckingham Palace event to mark the queen's birthday calling Nigeria and Afghanistan "possibly the two most corrupt countries in the world".

He was filmed making the remarks to the queen and Archbishop of Canterbury Justin Welby, ahead of an anti-corruption summit in London on Thursday where the Afghan and Nigerian presidents are expected.

"We've got some leaders of some fantastically corrupt countries coming to Britain," the prime minister said.

"Nigeria and Afghanistan, possibly the two most corrupt countries in the world," he added.

Welby, who worked as an oil executive in West Africa before joining the church and who has also undertaken conflict resolution work in Nigeria, noted that "this particular president is actually not corrupt".

"He's really trying," Cameron agreed, and the queen noted to Welby: "He is trying, isn't he?"

It was not clear to whom they were referring, but Nigerian President Muhammadu Buhari and Afghanistan's President Ashraf Ghani are both due to attend the summit.

In anti-bribery watchdog Transparency International's Corruption Perceptions Index for 2015, Afghanistan ranks 166th and Nigeria 136th out of 168 countries and territories.