Income tax, stamp duty and capital gains tax should all be reduced without rises in other levies, Mr Johnson said.
His call followed a series of clashes with Mrs May since his resignation from the Cabinet in July in protest at her so-called Chequers Brexit proposal.
In an article yesterday, the Uxbridge and South Ruislip MP wrote: “We should be looking not at rises but at cuts to income tax, capital gains tax and stamp duty. That is the way to get the economy going.”
Mr Johnson also criticised the Prime Minister and Chancellor Philip Hammond for threatening to increase taxes to fund an extra £20billion spending on the NHS.
“We do need to spend more on the NHS. We must find the extra £20billion that the Chancellor has rightly promised. We do need to step up our investments in the police and schools and other vital public services,” he wrote.
“But I am afraid I am not convinced that the answer is immediately to turn to the hardpressed taxpayer.”
He added: “I know it is not fashionable to point this out, but the US currently boasts economic growth rates far in excess of this country, at about 4.5 percent, with record low unemployment.
“That growth is being driven not just by the US government’s decision to cut taxes and regulation, but perhaps even more by psychology – by the sense that the government wants to cut taxes, wants to liberate and energise people. Do we send out that signal? I am not so sure.”
The Prime Minister’s spokesman insisted the Government had a record of tax reductions, saying: “I can point to this Government’s record of cutting taxes for hard-working households.”
Income tax thresholds had been raised to deliver a tax cut worth up to £1,000 for a basic-rate taxpayer and business taxes had also been reduced, the spokesman said. He also rejected claims from Mr Johnson’s allies that Downing Street officials had compiled a dossier detailing the former foreign secretary’s indiscretions.
“That is categorically untrue and offensive,” the spokesman added.