Britain is open for business, Theresa May told world leaders as she sought to convince them the UK was not looking inwards by pulling out of the single market.

Speaking at the World Economic Forum, the Prime Minister attempted to carve out a “truly Global” post-Brexit role for the UK.

Mrs May said Brexit would give Britain the chance to “step up to a new leadership role as the strongest and most forceful advocate for business, free markets and free trade anywhere in the world”.

Following boasts from the Foreign Secretary that countries were queuing up to do post-Brexit deals with the UK, Mrs May said Britain was already in talks with Australia, New Zealand and India.

And she added that China, Brazil and the Gulf States had also expressed in interest in striking deals.

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It follows Donald Trump’s suggestion that he would work “quickly” to reach a trade deal with the UK once it had left the EU and he wanted a deal done fast.

The Prime Minister attempted to convince her international audience gathered in the Alpine resort that the Brexit vote was a desire of the British electorate to reach out beyond Europe to deal with the rest of the world.

It struck a markedly different tone to her key Brexit speech in London on Tuesday when she told her UK audience: “But the message from the public before and during the referendum campaign was clear: Brexit must mean control of the number of people who come to Britain from Europe.”

However, Mrs May also sounded a stark warning on globalisation and urged leaders to “listen to those left behind”.

She cautioned of the “sense among the public that mainstream political and business leaders have failed to comprehend their legitimate concerns for too long”.

The Prime Minister, Theresa May, sets out her vision of 'a global Britain'. Video: In full: Theresa May’s Brexit speech

She said that Governments could help by intervening to make sure businesses doing well from globalisation shared the spoils.

Mrs May added: “…we must heed the underlying feeling that there are some companies, particularly those with global reach, who are playing by a different set of rules to ordinary, working people.”

But Mrs May was warned by German finance minister Wolfgang Schauble that world leaders would not take her seriously if carried out her threat to turn the UK into a low-tax economy to make it a more attractive place to do business than the EU.

The Prime Minister cautioned EU leaders on Tuesday that offering a Brexit punishment deal would be “an act of calamitous self-harm” and the UK would retaliate.

Mr Schauble said slashing taxes would break a G20 agreement.

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Mrs May’s speech came just hours after a blow to the City – as Europe’s biggest bank HSBC announced plans to move 1,000 UK-based jobs to Paris in two years’ time when Brexit comes into effect.

The move will trigger fears about a wider exodus from the financial sector, which accounts for 12% of Britain’s economy and employs over two million people.

The chairman of Japanese carmaker Toyota has also expressed concern about its UK operation, which employs 3,000 people.

However, the chief executive of Barclays Jes Staley told Radio 4’s Today programme: “I don’t believe that the European financial centre will leave the City of London.

“I think the UK will continue to be the financial lungs for Europe. We may have to move certain activities… but I think it’s going to be at the margin and will be manageable.”

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