Labour leader says lower tax and fewer regulations to attract investors would put businesses, jobs and public services at risk

Jeremy Corbyn has condemned the government’s threat to turn the UK into a low-tax economy if it cannot get a satisfactory Brexit deal, telling Theresa May that it would damage the UK and demeaned her office.

During a bad-tempered prime minister’s questions, the Labour leader repeatedly questioned May over the EU exit plan she set out in a speech on Tuesday. May responded by insisting she aimed to negotiate a strong deal and accusing Corbyn of having no vision of his own.

“There is indeed a difference between us,” the prime minister told him near the end of their exchange. “It’s very simple: when I look at the issue of Brexit, or indeed at any other issue, like the National Health Service or social care, I consider the issue, I set out my plan and I stick to it. It’s called leadership. He should try it some time.”

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Corbyn began the session by asking why May had outlined her plan at Lancaster House, rather than informing MPs in parliament. “Yesterday, the prime minister snubbed parliament and snubbed the Brexit committee recommendations to bring forward a white paper, while at the same time describing the referendum as a vote to restore our parliamentary democracy,” he said on Wednesday.

Referring to some newspapers’ comparisons between May and Margaret Thatcher, Corbyn said the prime minister was “not so much the Iron Lady as the Irony Lady”.

May responded by sidestepping the question to say she had set out “a vision for a stronger, fairer, more united, more outward-looking, prosperous, tolerant and independent Britain”. It was, she added, “a plan that will put the divisions of last year behind us”.

Corbyn condemned May for the section of her speech in which she warned the EU that if the UK did not get a sufficiently good deal it could reshape its economy to have lower tax and fewer regulations to attract investment.

“It won’t necessarily damage the EU, but it would certainly damage this country – businesses, jobs and public services,” the Labour leader said. “She demeans herself and her office, and our country’s standing, by making these kind of threats.”

May was dismissive of Corbyn’s comments, returning to the issue of his party’s occasionally confused stance over Brexit. “I’ve got a plan, he doesn’t have a clue,” she said. The prime minister gave no new details of what her Brexit plan might involve, even when questioned by Corbyn several times about whether a deal to keep access to EU markets might include making payments.

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“It is about the best possible access for British business to operate in the European Union member states, and for European businesses to operate here in the United Kingdom,” May said. “It’s about sitting down and negotiating the best possible deal for the United Kingdom. That’s what I’m committed to and that’s what this government is going to deliver.”

Angus Robertson, the SNP’s Westminster leader, also questioned May about Brexit, asking if her government was “stringing the people of Scotland along” by promising they would be an equal partner in Brexit while refusing any special Scottish deals.

His SNP colleague, Kirsty Blackman, gleaned one small piece of information in asking May whether the passage of the so-called great repeal bill, which would see EU law moved into British legislation as Brexit happened, could see non-English MPs excluded from some votes.

May confirmed that the English votes for English laws provision would apply: “If any part of it only applies to England, then it will be subject to English votes on English laws.”