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British Prime Minister David Cameron called Nigeria and Afghanistan "possibly the two most corrupt countries in the world" in inadvertently public remarks on Tuesday, as Queen Elizabeth II was caught making her own gaffe about a "rude" Chinese delegation.

Cameron was filmed making the remarks to the queen and Archbishop of Canterbury Justin Welby at an event at Buckingham Palace, ahead of an anti-corruption summit he is hosting in London on Thursday.

"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.

'Undiplomatic' Chinese

At a separate garden party event on Tuesday, the queen was caught on camera describing the delegation for a Chinese state visit last year as "rude".

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

D'Orsi was recorded as saying, "I'm not sure whether you knew, but it was quite a testing time for me," to which the queen replied that she did know, before adding that members of the Chinese delegation "were very rude to the ambassador".

The police commander agreed, saying, "It was very rude and very undiplomatic I thought". It was not clear which members of the delegation they were referring to.

Beijing and Chinese state media at the time hailed the visit as a high watermark in Sino-British relations.

There was no immediate response from Chinese officials to Tuesday's remarks, while the Daily Mail cited Buckingham Palace as saying it would not comment on the queen's private conversations.

"However the Chinese State Visit was extremely successful and all parties worked closely to ensure it proceeded smoothly," the British newspaper quoted a spokesman as saying.