Farage, the Brexit-campaigner and self-described troublemaker, is a friend of Trump and was at his election victory party in Florida.
He has offered to act as an interlocutor between the British government and the Trump administration, which takes power in January.
The Treasury minister Darren Jones said that the government would likely reject that offer.
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Governments around the world are trying to figure out how to deal with Trump, who has promised to increase tariffs and whose first four-year term was characterised by a protectionist trade policy and isolationist rhetoric, including threats to withdraw from NATO.