Jacob Rees-Mogg has launched an extraordinary attack on a doctor helping to plan for a no-deal Brexit who warned that people will die if it goes ahead.

Dr David Nicholl, a consultant neurologist, helped draft the devastating Operation Yellowhammer document which predicted shortages of medicines, food and fuel.

Now a whistleblower, Dr Nicholl asked the Commons leader: “What level of mortality rate are you willing to accept in the light of a no-deal Brexit?”

But Mr Rees-Mogg insisted nobody would die if the UK crashes out of the EU with no agreement – and turned on the neurologist, accusing him of “the worst excess of Project Fear”.

“I’m surprised that a doctor in your position would be fear-mongering in this way on public radio,” he alleged, in the exchange on LBC radio.

“I think it’s deeply irresponsible, Dr Nicholl, of you to call in and try to spread fear across the country. It’s typical of Remainer campaigners to try and you should be quite ashamed, I’m afraid.”

When Dr Nicholl replied: “Can I remind you I wrote the plans in mitigation?”, Mr Rees-Mogg lashed out by accusing him of being incompetent.

“Well, you didn’t write very good plans if you hadn’t worked out how to mitigate, had you? It’s fortunate that they’re being written by other people now who are serious about mitigating and not remoaners,” he told the doctor.

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The comments were attacked by Gina Miller, the anti-Brexit campaigner, who urged everyone to listen to the exchange.

“Having spoken to many politicians over recent months, I’ve been saying that this government has little regard for the human cost of Brexit,” she tweeted.

And Dr Paul Williams, a Labour supporter of the anti-Brexit Best for Britain group, said: “This exchange shows how little regard the government has for those who rely on access to medicines. Their reckless pursuit of a no-deal Brexit is putting lives at risk.”

Dr Nicholl also accused Michael Gove, the cabinet minister, of misleading the public when he claimed the stark problems outlined in the Yellowhammer dossier were “a worst-case scenario”.

He insisted they were the planners’ best guess of what will happen – after the government appeared to admit the document, far from being “out of date”, as claimed, dated from the start of August.

At the weekend, The Sunday Times revealed that doctors had warned the NHS to brace itself for the “biggest threat it has ever faced” if the UK leaves the EU without a deal.

Confidential files seen by the newspaper revealed lists of drugs it has been impossible to stockpile, putting patients at potential risk.