The shadow chancellor laid into the Prime Minister on the Andrew Marr show on Sunday as he suggested Mrs May’s vow to walk out of the negotiations if European Union leaders try to punish Britain would backfire.
In a stark warning to Brussels after revealing her Brexit blueprint, the PM said: "No deal for Britain is better than a bad deal for Britain.”
Blasting Mrs May for her boldness, Mr McDonnell insisted the alternative of leaving the negotiation table would turn the UK into a tax haven for cooperations.
He told the BBC programme: “What it would mean is setting us up as a tax haven.
Theresa May was accused of ‘exaggerating a dangerous threat’ ahead of Brexit
“That would effectively cut us off from the rest of Europe and would actually cause us problems with other trade agreements across the world, it would destroy our industrial base and undermine our services as well.
“I think it is a hollow threat but I also think it is a dangerous threat, that is not the way you go into these negotiations.”
The Labour Party MP continued: “Yes, you need to go in will a little bit of strength but to exaggerate a threat like that which is unrealisable and remember what it means as well, it means cutting our cooperation taxes down to 12.5 per cent which is the Irish rate, how then are we going to fund our public services and the NHS?”
Mr McDonnell also denied that Labour is preparing to lose a pair of crunch by-elections next month as the party continues to crumble under Jeremy Corbyn’s leadership.
What it would mean is setting us up as a tax haven
Ukip leader Paul Nuttall has made a bid for his anti-EU party to take over the Labour heartland constituencies, as he decided to stand in Stoke, which he described as "the capital of Brexit”.
Defeats for Labour in Stoke-on-Trent Central and Copeland on February 23 would be unprecedented in the history of by-elections, which almost never see Opposition parties lose seats during a Government's term in office.
The shadow minister said: "Since Brexit you can't calculate by-election results on what's gone on in the past so what we're going to do is fight for every vote, and that's what we're going to do.
"I'm angry by the statements by Mr Nuttall today, that's taking Stoke for granted – he's basically saying he's going to win it. You don't take the election for granted."
Mr McDonnell’s refusal to acknowledge the possibility of defeat and condemnation of Theresa May’s willingness to fight for the best possible deal for Britain comes as the PM told Marr she will be travelling to the US to meet with President Donald Trump on Friday.
May's Brexit speech: Europe reacts
Tue, January 17, 2017
Politicians and celebrities tweet their reaction as Theresa May unveils her 12 point plan for Britain leaving the EU.
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The British Prime Minister Delivers Her Brexit Speech
Mrs May, who is set to be the first foreign leader to meet with Mr Trump after his inauguration on Friday, said: “We can look at areas even in advance of being able to sign a formal trade deal. Perhaps we could look at barriers to trade at the moment and remove some of those barriers to open up that new trading relationship.”
Despite President Trump delivering a thundering speech at his inauguration where he vowed to put America first, the PM said she was “confident” of striking a trade deal.
She told the BBC host: “I think his inauguration speech had a very clear message to it, which is the message that he gave during his campaign, about putting America first.
“But if you think about it, any leader, any government as we do here in the United Kingdom, when we look at any issue, we ensure we’re putting the UK’s interests and interests of British people first.
“I shall be meeting him on Friday and talking to him. There will be many issues for us to talk about because obviously, the special relationship between the UK and the US has been strong for many years.