Under one option, a "new customs partnership" would succeed the current customs union, which the UK government said would remove the need for a customs border with the EU but still leave it free it to strike new trade deals with other countries.

Under the other, technology and bureaucracy would combine to create a "streamlined" and "frictionless" customs border between the UK and EU to minimise the impact of Brexit on trade and commerce.

The plans, published on Tuesday in a long-anticipated position paper, also contemplate a temporary customs union with Europe following Brexit, to give countries more time to put border checks and infrastructure in place after the UK leaves the European Union in March 2018.

But the government's plan - which it admitted was "unprecedented" - has already faced criticism from many sides.

Some called it wishful thinking from "the territory of wanting to have their cake and eat it", and others calling it a "Brexit betrayal" against the will of the British people.

The UK also wants the freedom to strike new trade deals with other countries such as Australia during the transition phase - deals which would come into effect once the transition is over.

Brexit secretary David Davis could not say how long the temporary arrangement would last. He estimated to the BBC "something like two years, maybe a bit shorter", and said it would end by 2022 at the latest.

The paper also sets out two alternatives for a permanent customs arrangement with the EU. It does not say which the government prefers, calling them "two broad approaches the UK could adopt" depending on negotiations with the EU.

Under one, a "highly streamlined customs arrangement", the UK and EU would use "technology-based solutions" to make it easier for businesses to satisfy new requirements and procedures when moving goods across the border.

Under the other, the UK would sign a "new customs partnership" with the EU that would eliminate the need for a border - for example mirroring EU requirements for imports from the rest of the world where the final destination is the EU.

International Trade Secretary Dr Liam Fox said leaving the customs union would allow Britain to generate "fully independent trade policy".

"We will seek a new customs arrangement that ensures that trade between the UK and the EU remains as frictionless as possible and allows us to forge new trade relationships with our partners in Europe and around the world," he said.

A European Commission spokesman they would study the UK position paper ahead of the next round of negotiations at the end of August.

However they do not want to start talking about customs plans until they have made more progress on talks over the "divorce bill" - an agreement on the Brexit financial settlement as well as issues including the rights of EU citizens in the UK.

"We take note of the UK's request for an implementing period and its preferences as regards the future relationship, but we will only address them once we have made sufficient progress on the terms of the orderly withdrawal," the spokesman said.

"An agreement on a future relationship between the EU and the UK can only be finalised once the UK has become a third country??? 'frictionless trade' is not possible outside the single market and customs union."

The EU is also working on a position paper on the customs union.

Mr Davis said during the transition period Britain would be able to negotiate new trade deals.

"We should be able to have an arrangement where we can do the negotiations, sign it off, but not enter into effect," he said.

But former European commissioner for trade Karel de Gucht told the BBC he doubted the EU would agree to a temporary customs union if it also meant Britain could start working on other trade deals.

Otherwise the EU would effectively be agreeing to help the UK undercut EU tariffs, he said.

Instead, he predicted, the EU would want the UK to stay in the customs union on its own terms: paying contributions to the EU budget and not seeking to sign other trade deals.

"It's a quagmire, you know," he said.

Ireland's EU commissioner Phil Hogan told the Financial Times that Dublin could block a customs deal unless the problem of the Northern Ireland border was satisfactorily solved.

"There's a high level of delusion in London at the moment about what is required to be done," Mr Hogan said.

The government is expected to publish its plan for the border on Wednesday.

The customs plan is being seen as a concession towards a 'soft Brexit' that has been sought by companies and other groups worried about the impact of a rushed exit from Europe.

The Federation of Small Businesses said it "would give small businesses the time they need to prepare for new customs arrangements, which is very welcome".

But the official Leave campaign called it a "Brexit betrayal", saying it was a "stitch-up to delay global trade for years".

"When 17.4 million voted Leave last year we wanted to control our destiny as a trading nation," the Leave.EU Twitter account said. "This new plan is a disgrace!"

Former UKIP leader Nigel Farage said "I warned of the great Brexit betrayal two weeks ago. It is now official government policy."

Labour's Shadow Secretary of State for Exiting the European Union Keir Starmer said the government's plans were "incoherent and inadequate proposals designed to gloss over deep and continuing divisions within the cabinet".

And anti-Brexit Labour MP Chris Leslie told Politico the government had returned "to the territory of wanting to have their cake and eat it".

"It is a fantasy to pretend we can have the freest and most frictionless trade possible with our largest partner when the government remain intent on pulling Britain out of the customs union," he said.

"This is wishful thinking of the highest order."

Guy Verhofstadt, the European Parliament's chief Brexit negotiator, also suggested the UK's plan was unrealistic, Tweeting: "To be in & out of the Customs Union & 'invisible borders' is a fantasy."