Such revelations have sparked a push by the OECD, the Paris based group of countries that aims to promote sustainable growth, to stop internet companies moving profits from one company to another to cut tax bills.
George Osborne, the U.K. chancellor, has also announced a crackdown", unveiling a 25 percent levy on diverted profits which his allies described as the "Google tax".
Mr Barzun said: "My hope is that if those rules change, they will play by those rules as well."
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President Barack Obama said in June that companies which avoid tax in the US by taking up residency in havens were "essentially renouncing their American citizenship".
Mr Barzun also defended Facebook against claims by British politicians that the company withheld information on potential terror suspects as part of an official report into the jihadi inspired murder of Fusilier Lee Rigby 18 months ago. Members of the intelligence and security committee have warned that new encryption methods used by technology companies hamper the government's attempts to monitor communications.
He said: "I don't think it is fair to pin everything on the private sector." Though he added: "Nor is it fair to say they have no responsibility in trying to come up with solutions."
Taxation has become a thorny issue in the US-UK relationship, which Mr Barzun described as "vibrant, versatile and vital".
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While Boris Johnson has pursued the US embassy for several years over unpaid fees for the London congestion charge, the London mayor himself has recently admitted that he is being pursued by the US tax authorities for unpaid capital gains tax.
Mr Barzun defended his embassy's policy of not paying the charge, the payments for which have now mounted to more than £8 million. He called the charge a tax, insisting that countries should not tax foreign embassies. But he was less forgiving of the situation faced by Mr Johnson, who admitted last month that he is being pursued by the Internal Revenue Service on the basis that he is a U.S. citizen.
While Mr Barzun said he did not want to comment on Mr Johnson's personal circumstances, he added: "We have our rules and we expect people to play by them.
"If you have the benefit of being an American citizen, you have to pay your fair share of taxes — that's the general point."