•John Bolton said the US supported a no-deal Brexit and added that Washington would propose an accelerated series of trade deals.
•According to Mr Bolton, a bilateral agreement or "series of agreements" could be carved out "very quickly, very straight-forwardly".
The UK is "first in line" for a trade deal with the US, President Trump's National Security Adviser has said.
John Bolton said the US supported a no-deal Brexit and added that Washington would propose an accelerated series of trade deals.
According to Mr Bolton, deals could be done on a "sector-by-sector" basis, with an agreement on manufacturing being agreed first.
His comments came after meeting Prime Minister Boris Johnson at No 10.
According to Mr Bolton, a bilateral agreement or "series of agreements" could be carved out "very quickly, very straight-forwardly".
While saying that "both President Trump and I were leavers before there were leavers", he added that a trade deal for financial services and agriculture would not be the first to be agreed.
Mr Bolton said "doing it in pieces" is not unprecedented and the US understood the importance and urgency of "doing as much as we can agree on as rapidly as possible because of the impending 31 October exit date".
He argued that there would be enthusiastic bipartisan support in Congress for speedy ratification at each stage.
"To be clear, in the Trump administration, Britain's constantly at the front of the trade queue, or line as we say," said Mr Bolton.
"We want to move very quickly. We wish we could have moved further along in this with the prior government."
When asked whether his proposed plan would follow World Trade Organisation rules, he said "our trade negotiators seem to think it is".
He also criticised the European Union and accused them of treating voters like "peasants".
"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," he said.
He made it clear that the US government "fully understands" that Brexit is the UK's first priority, and said issues like Iran, China, and the involvement of the Chinese telecoms firm Huawei in building the UK's 5G mobile infrastructure could be put off until after the UK leaves the EU.
"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," he said.
Mr Bolton also referenced Mr Johnson's willingness to participate in Operation Sentinel, which aims to beef up the military presence in the Gulf in the face of tensions between the West and Iran, saying he was "pleased" as this "reflects a change from the prior government".
Chairman of the Foreign Affairs Committee Tom Tugendhat said it was important to remember that Mr Bolton was a strong advocate of "America first".
"This isn't some sort of dewy-eyed, soft, romantic vision of a special relationship that he's trying to kindle for romantic and historic reasons," he told BBC Radio 4's Today programme.
"He has a very specific interest which is to defend and extend US interests."
Mr Johnson is expected to have his first face-to-face meeting as prime minister with Mr Trump later this month at the G7 summit in France.