UK will be 'first in line' for a trade deal with the US
Speaking following a meeting with Prime Minister Boris Johnson on a visit to London, Mr Bolton said: "A prior American president said that if the United Kingdom left the European Union, it would go to the back of the queue on trade deals.
"To be clear, in the Trump administration Britain's constantly at the front of the trade queue, or line as we say."
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Hide AdMr Bolton attacked the EU and said the UK's decision to leave the bloc should be respected.
He said: "The fashion in the European Union when the people vote the wrong way from the way that the elites want to go is to make the peasants vote again and again until they get it right."
Mr Bolton said it is "hard to imagine" people in the UK did not know "what was at stake" when they voted to leave the EU in 2016.
Mr Bolton said the US had been "ready to negotiate" with Theresa May's government and that the US could do a trade deal with the UK "in pieces".
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Hide AdHe said: "We want to move very quickly. We wish we could have moved further along in this with the prior government.
"We were ready to negotiate. We are ready to negotiate now."
Mr Bolton said the countries could concentrate on areas they can agree on first.
He said: "The idea of doing it in pieces rather than waiting for the whole thing is not unprecedented.
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Hide Ad"I think here we see the importance and urgency of doing as much as we can agree on as rapidly as possible because of the impending October 31 exit date."
Asked whether piecemeal trade agreements like this are allowed under WTO rules, Mr Bolton said: "Our trade negotiators seem to think it is."
Prime Minister Boris Johnson joined a meeting with US National Security adviser John Bolton where Brexit, Iran, Hong Kong and 5G were discussed, Downing Street said.
A Downing Street statement said: "The Prime Minister joined a meeting at Downing Street today between senior officials and US National Security adviser John Bolton.
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Hide Ad"They discussed the close UK-US trading relationship and our shared commitment to an ambitious free trade agreement once the UK leaves the EU.
"They also spoke about Brexit and a range of other issues - including Iran, Hong Kong and 5G."
Mr Bolton said issues like Iran, China and Huawei could be put off until after Brexit.
He said: "The message I wanted to convey on Iran, and on some other issues in which I include China, 5G, Huawei, that cluster of issues, is that the President and the US Government fully understands that in the next few days the UK Government has a singular focus on the Brexit issue, so that we are not hoping for anything on these broad and complex questions.
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Hide Ad"We just ask that, as issues come up, we resolve them individually and we reserve the time to have a larger conversation on some of these important issues at a moment that is really right for the new government. We just felt we owe them that.
"Obviously we have views on these issues, I think that is appreciated by the new government. They said in particular that looking really from square one on the Huawei issue that they were very concerned about not having any compromise in the security of telecommunications in the 5G space."
He added: "We don't want to put you under pressure on these issues. There will be time enough to talk, that is really all we ask for."