It would see Britain follow EU rules on goods to protect cross-border trade and avoid checks on the Irish frontier, while enabling it to control migration and sign new non-EU trade deals, including in services.

But the idea of staying tied to the bloc for years after Brexit prompted two ministers to quit her cabinet this week, and has revived talk of a leadership challenge in May's Conservative party.

When the details were finally published in a 98-page document Thursday, eurosceptic MPs were quick to condemn the plan -- aided by Donald Trump.

As he headed to Britain for his first official trip, the US president said that "I don't know that this is what [people] voted for" in the Brexit referendum in 2016.

The plan won support from some business groups, but the City of London warned its provision for looser ties for financial services were a "real blow" for the all-important sector.

During the launch of the plan, the House of Commons was briefly suspended by Brexit Secretary Dominic Raab due to heckling.

MPs were angry they had not seen the document beforehand, prompting the speaker to give them five minutes to find a copy.

Raab -- who was appointed on Monday after his predecessor David Davis quit, followed by foreign minister Boris Johnson -- then faced more jeering as he said that a "deal was within reach" with Brussels.

The response from the European Union, which must ultimately agree the deal, was cautious with chief negotiator Michel Barnier saying on Twitter that he would analyse the proposals.

The Irish government said it hoped the paper could "inject momentum into negotiations", with both sides still hoping for a deal by October.

Privately, EU diplomats indicated there was still a long way to go.

"We have to walk the tight rope between welcoming the act of the UK making an offer while also making it clear that this offer will not do and will need a lot of work from the British government," one said.

- 'Not a solution' -

Britain voted for Brexit in June 2016, but May has been unable to present a detailed plan to Brussels until now because of the deep divisions in her government.

"We should welcome this. It marks an obvious move by the government to try to get the negotiations going," said Anand Menon, director of the UK in a Changing Europe think-tank based at King's College London.

"Equally, it's not a solution. I don't see the European Union accepting it."

May had briefed a number of European leaders on the plan before it was published, including EU president Donald Tusk and German Angela Merkel.

But the EU has repeatedly warned it cannot accept any "cherry-picking" of its single market and its four freedoms, of movement, capital, goods and services.

May is also likely to have a tough time getting the plan through parliament, with the right-wing of her Conservative party increasingly rebellious.

MP Jacob Rees-Mogg, who leads a powerful eurosceptic group, said he could not vote for the plan.

Britain would have to follow EU rules that it could not influence, and despite claims that parliament could reject any new regulations, the repercussions were such that in reality it "will have no say".

"Taken as a whole, this recreates many of the worst aspects of the EU the British people voted to leave," he said.

- 'Real blow' for City -

It also fulfils promises to the EU not to allow a "hard border" between British Northern Ireland and Ireland.

The CBI business lobby welcomed the direction of policy, but warned there were gaps in the plan -- while the City of London was scathing.

Policy chairman Catherine McGuinness said the proposal for looser ties was a "real blow for the UK's financial and related professional services sector".

The opposition Labour party says a new customs union with the EU is the answer, condemning May's plan as a "bureaucratic nightmare".afp