Jeremy Corbyn has accused Theresa May of "demeaning" her office and her country by threatening to make the UK an offshore tax haven if she cannot get the Brexit deal she wants from the EU.

The Prime Minister denied the Brexit plan she unveiled on Tuesday was based on threats, insisting she had set out a vision for "a stronger, fairer, more united, more outward-looking, prosperous, tolerant and independent, truly global Britain".

The exchange at Prime Minister's Questions in the House of Commons came after Brexit Secretary David Davis said Britain may not have fully freed itself from European Union rules until 2021.

Read more: In full - Theresa May's Brexit speech

Speaking on BBC Radio 4's Today programme, Mr Davis brushed aside suggestions that MPs might vote down a deal thrashed out over the next two years under Article 50 of the EU treaties, insisting: "I intend to make this a success."

He said he was "very determined' to agree a divorce deal with Brussels and a new trading relationship within the two-year deadline, and said Britain would not be "supplicant" to any EU demand to extend the negotiation period.

The man who will lead the European Council when negotiations begin - Maltese prime minister Joseph Muscat - warned that the negotiations would be "arduous" and that any deal offered to the UK must be "inferior" to the terms it could have as a member.

"We want a fair deal for the UK but that deal necessarily needs to be inferior to membership," Mr Muscat told the European Parliament in Strasbourg.

"This should not come as a surprise to anyone. Indeed, thinking it can be otherwise would indicate a detachment from reality."

Foreign Secretary Boris Johnson warned the remaining EU nations not to pursue a punitive approach to the Brexit negotiations.

Responding to comments from an aide to French President Francois Hollande, who said Britain should not expect a better trading relationship with Europe from outside the EU, Mr Johnson said: "If Monsieur Hollande wants to administer punishment beatings that anyone chooses to escape, rather in the manner of some World War Two movie, then I don't think that's the way forward.

Read more: In full - Theresa May's Brexit speech

"It's not in the interests of our friends or our partners."

Mrs May used a high-profile speech at Lancaster House in London on Tuesday to announce she will take Britain out of the European single market and may also quit the customs union, while seeking a free trade agreement with the EU to allow UK companies to continue doing business with its 27 remaining members.

She made clear that she was ready to walk away from a "punitive" deal, warning EU partners that Britain could use low corporate taxes to attract business and investment from around the world if it could not strike a favourable trade deal with Europe.

Speaking at PMQs in the Commons, Mr Corbyn called on the PM to "stop her threat of a bargain basement Britain, a low-pay tax haven on the shores of Europe".

The Labour leader said: "It wouldn't necessarily damage the EU, but it would certainly damage this country - businesses, jobs and public services.

"She demeans herself and her office and our country's standing by making these kinds of threats."

He accused the PM of failing to guarantee the future of thousands of EU nationals working in UK public services or to explain whether she would be willing to pay for continued access to the single market.

Mrs May responded: "Access to the single market is exactly what I was talking about yesterday in my speech. One of the key principles, the key objectives, is that we negotiate a free trade agreement with the EU that gives us the widest possible access for trading with and operating within the EU."

Mr Davis confirmed that the Government was expecting an implementation period after the Article 50 talks, during which new arrangements on issues like borders, customs and regulations could be introduced at different times.

Read more: In full - Theresa May's Brexit speech

"We've said we accept that there may be an implementation phase thereafter," he told Today.

"It won't be a long time... a year or two."

MPs and peers will get a final vote on whatever deal the UK reaches with the EU, but they will not be able to stop Brexit happening, Mr Davis said.

He insisted Parliament would not vote down the deal he secures with the EU.

"I intend to make this a success," he said.

"Parliament, remember, gave the decision on leaving to the people, by a vast majority it decided it was the people who made the decision in the referendum, so it's not for Parliament to reverse that.

"So at the end of the day, they will end up deciding on the mandate."

Asked if Britain would revert to World Trade Organistion rules if Parliament rejects the deal, Mr Davis said: "They won't vote it down, this negotiation will succeed."

Mr Davis insisted there would be no difference in Britons' right to travel in Europe or vice versa but admitted new customs checks could come into force for lorries carrying goods into or out of the UK.

Mr Davis dismissed warnings from the European Parliament's lead negotiator, Guy Verhofstadt, that Britain will not be able to enjoy better terms after Brexit than it has within the EU, and that it cannot "cherry-pick" which aspects of membership it wants to keep.

Mr Verhofstadt was "one player of several" and the "more important" president of the European Council, Donald Tusk, had described Mrs May's plan as "realistic", he said.

Mr Davis dismissed suggestions that Britain did not have enough numbers or experience in its Civil Service to deal with Brexit, revealing that former cabinet secretary Lord Butler told him: "Our Civil Service can cope with World War Two, they can easily cope with this."