Mr. Osborne in particular sees Britain’s future as a trading nation tied up with a rising and wealthy China. He has made great efforts to praise Beijing and even “take a bit of a risk with the China relationship,” as he said, by visiting the restive Xinjiang region, where Uighur separatists have been repressed by the central government.

Britain, Mr. Osborne said, wanted to be “China’s best partner in the West,” even as the Chinese economy is slowing, and he has tried to prove it, causing frustration and even anger in Washington, especially as Mr. Xi has cracked down on dissent and censored the Internet.

China, like Russia, regards the European Union as an artificial political construct and emphasizes bilateral relations with different countries, sometimes setting one off against another.

Germany, too, has not been above putting its economic interests before those of other Europeans. In one prominent example, the country undermined the position of the European Commission last year in a tariff dispute with China over the import or “dumping” of cheap solar panels. Germany was not alone in opposition, but it weakened the commission’s negotiating stance before a minimum price for the panels was set.

Chancellor Angela Merkel of Germany has also been accused of playing down human rights for economic interests, and she inevitably brings with her to China high-level German business representatives.

But she has been more outspoken about noneconomic issues than the British have been. Being more important to China than Britain, and given its history, Germany does not keep entirely silent about Chinese abuses, but the criticism is rarely public. Mr. Xi made a major visit to Berlin in 2014 and praised Berlin and Beijing as “two pillars of growth in Asia and Europe.”

Ms. Merkel briefs reporters on her conversations with the Chinese, which inevitably include at least nominal discussions about human rights and especially cybersecurity and the Chinese hacking of German companies.