There should be no border posts between Ireland and the British province of Northern Ireland after Brexit, Britain said in an early attempt to resolve one of the most complex aspects of its European Union exit.

Some 30,000 people cross the 500 kilometre border every day without customs or immigration checks, testing negotiators who have to work out how to tighten controls without inflaming tensions in a region where around 3,600 people were killed before a peace agreement in 1998.

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An American tourist stands near the Houses of Parliament the day after the majority of the British public voted to leave the European Union on June 25, 2016 in London, England.

The British government said in a paper due to be published on Wednesday that it wanted a seamless and frictionless frontier without "physical border infrastructure and border posts," arguing that new customs arrangements it proposed on Tuesday would allow the free flow of goods.

The issue of how the Republic of Ireland and Northern Ireland will fare is particularly sensitive given the decades of violence over whether it should be part of Britain or Ireland.

"Both sides needs to show flexibility and imagination when it comes to the border issue in Northern Ireland," a British government source said.

Britain put forward two options for future customs arrangements with the EU on Tuesday, the first would involve no customs border at all, while a second detailed "highly-streamlined" customs checks.

However, the idea met with scepticism among some of Britain's soon-to-be former EU partners, with one EU official describing the idea of an invisible border as "fantasy."

"We have some very clear principles. Top of our list is to agree upfront no physical border infrastructure — that would mean a return to the border posts of the past and is completely unacceptable to the UK," the British source said.

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