The influential backbencher said the chancellor Philip Hammond would be moving into “dangerous territory” if he broke away from the Conservative manifesto pledge to keep taxes low.
Mr Rees-Mogg, who chairs the pro-Brexit European Research Group, also insisted that a “Brexit dividend” could help to pay for the cash boost, referring to the money Britain could claw back from Brussels after leaving the EU.
In a major speech last week, Theresa May set out plans for a £20bn-a-year cash injection for the health service in England.
However she drew criticism from Tory MPs and from independent experts for saying it could be paid for in part by a Brexit dividend and failing to say which taxes might be hiked to fund the boost.
Mr Rees-Mogg also drew a comparison with the chancellor’s embarrassing U-turn on national insurance contributions in last year’s Budget, when he was forced to back down on plans to hike payments for the self-employed, in breach of a Conservative manifesto commitment.
“This country is as highly taxed as a percentage of GDP as it has been since the early 1970s, late 1960s,” he told LBC.
“I don’t think the Conservative party is here to increase taxes. Philip Hammond seems to think otherwise but he hasn’t yet presented a Budget and he may find there is not a lot of support for tax increases.
“He did try it before. He tried to increase national insurance – and he had to back down – which was a clear attack on the self-employed and was a great mistake.
“I think you make money available to the NHS by growing the economy and I think you grow the economy by lower tax rates. I think you stifle the economy by higher tax rates.”
Mr Rees-Mogg said part of the increase for the NHS would be funded by £10bn the UK currently send to Brussels, while the deficit had also reduced, offering additional “room for manoeuvre”.
He added: “The Tory party manifesto said the right thing on taxes. If you say things in the manifesto that you then don’t do, the electorate boots you out.
“I think it is really dangerous territory not to stick to the principle of your promise as well as the small print.”
The new NHS funding has emboldened several ministers to push for more cash for their departments in the autumn Budget.
Gavin Williamson reportedly threatened to bring down the government unless defence spending was increased.
However allies of the defence secretary move to quash reports in the Mail on Sunday that the former chief whip boasted “I made her, and I can break her”.
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