The party’s economic spokesman confirmed the change as part of the first Budget that Reform would implement in their first 100 days in Government at the Reform UK National Conference.
The increase would be the single largest increase to the tax-free allowance in history, saving the majority of taxpayers around £500 a year.
The change would also take 2.9 million people out of income tax and benefit 40 million people overall.
The state pension would also remain untaxed thanks to the change.
Mr Jenrick promised to deliver the increase in his first Budget and to hold that Budget within 100 days of a Reform government being elected.
He also announced that Reform’s ambition is to continue to increase the tax-free allowance.
He added: “I will go further, step-by-step, until we’ve reached Reform’s ambition of a £20,000 tax free allowance.That is my mission.”
The change would come after a five-year freeze on the tax-free allowance under both Labour and Tory governments, which has left the allowance £3,500 lower than it would have been otherwise.
The increase would cost £17.7billion in the first year, rising to £21bn by the fifth year of the Parliament and would be funded by £80bn in savings Reform has already identified.
Robert Jenrick has announced that Reform UK will increase tax-free allowance at the Reform UK National Conference in Birmingham
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That includes £52bn from welfare reform, £7bn a year by cutting the foreign aid budget, £10bn by ending net zero subsidies, £7bn by reducing civil servant and Quango headcount.
Mr Jenrick made his speech at the Reform UK National Conference in Birmingham.
He said: “There has never, in our lifetimes, been a worse time to be a worker in Britain.
“As chancellor, I will wake each morning with one purpose. To make Britain a better place to be a worker than it was the day before.
Robert Jenrick’s first budget would come within 100 days of Reform taking over Government
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“In the first hundred days of a Reform government, in our first Budget, we will raise the tax-free personal allowance from £12,570… to £15,000.”
He also challenged Prime Minister Andy Burnham to match his commitment and said: “The hard choice for Burnham and for us is exactly the same. It’s either welfare waste, foreign aid and migrants — or the British worker.
“We choose the worker.
“When we can — only when it is paid for in full — I will go further, step-by-step, until we’ve reached Reform’s ambition of a £20,000 tax-free allowance.”
Mr Jenrick also said that he would resign should he not be able to reach £15,000.
He told the audience: “In the real world, if you fail, you’re gone. So, hear me. If I don’t deliver this, I – will – resign. No ifs, no buts. I’ll be gone.”
The announcement comes just a day after Richard Tice set out policy on electricity and gas bills, scrapping carbon taxes on generators and permanently removing VAT from consumer energy bills.
The plan includes removing the tax on gas generators from the UK Emissions Trading Scheme and the Carbon Price Support.
Mr Tice also set out the party’s intention to repeal a number of policies which they claim will increase gas and electricity bills, such as the Renewables Obligation, Feed-in Tariffs, Warm Homes Discount and Green Gas Levy.
They say these represent an extra £80 on household energy bills.