The Commons leader angered MPs when he stepped up his war on whistleblower Dr David Nicholl, a consultant neurologist, after a bitter clash earlier this week.
“I’m afraid it seems to me that Dr David Nicholl is as irresponsible as Dr Wakefield,” Mr Rees-Mogg claimed.
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“What he had to say, I will repeat it, is as irresponsible as Dr Wakefield in threatening that people will die because we leave the European Union. What level of irresponsibility was that?”
The highly-respected Dr Nicholl was asked, by the last government, to help draw up the devastating Operation Yellowhammer document, predicting shortages of medicines, food and fuel after a crash-out Brexit.
Dr Wakefield, meanwhile, was struck off the UK medical register for unethical behaviour after his discredited research linked autism to the measles, mumps and rubella (MMR) vaccine.
The claim led to parents stopping their children being immunised and an increase in measles cases. The UK recently lost its measles-free status.
“Absolutely disgusting for @Jacob_Rees_Mogg to slander such a highly respected NHS consultant and whistleblower as @djnicholl from behind the cowardly screen of parliamentary privilege,” she tweeted.
The latest controversy comes amid growing criticism of Mr Rees-Mogg, whose behaviour has been blamed for fuelling the Tory civil war over Brexit.
He was labelled the “embodiment of arrogance, entitlement and contempt for parliament” after lying down on the Commons front bench during a key debate.
Some of the 21 rebels who sank Boris Johnson’s hopes of defeating the backbench bill to block a crash-out Brexit said they ploughed ahead with their revolt because of him.
And Phillip Lee, when dramatically defecting to the Lib Dems on Wednesday, said Mr Rees-Mogg’s attack on Dr Nicholl had “tipped him over the edge”.
“It was disgraceful, it was about ignoring evidence, it was about showing disrespect to experts, to people with professional standing and knowledge,” Dr Lee protested.
In the clash on live radio, Dr Nicholl had 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.
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.