However, under United Kingdom electoral commission rules, May will continue in her post in an acting capacity until 23 July when the party picks a successor, who will also become Britain's next prime minister.
Mr Johnson, a leading campaigner in the 2016 referendum who quit the government previous year over Mrs May's plan, is among several would-be candidates who say they are willing to do this.
May was forced to strike a deal for support with Northern Ireland's pro-Brexit Democratic Unionist Party, and since then has struggled to keep her party and its allies together.
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Over the following days more than 300 Conservative MPs at Westminster will vote on the long list of names, using a process of elimination until only two names are left.
Despite the loss, Farage said the result showed that British politics has "fundamentally changed", with the stranglehold of Conservative and Labour now broken. She announced her decision to quit as prime minister last month.
Boris Johnson, former foreign secretary and leading Brexiteer, is the favourite among 11 candidates to replace May in the two-phase leadership election.
Unite activist Lisa Forbes won the seat with 10,484 seats ahead of the Brexit Party's Mike Greene who had 9,801 votes.
UK Prime Minister Theresa May resigns as leader of the Conservative Party on June 7th.
Conservative lawmakers held a secret ballot yesterday, with any candidates who don't get at least 5 per cent dropping out.
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Killing Eve " follows the same format as BBC Sounds' Line of Duty companion podcast series, which regularly topped the charts. ' Killing Eve ' is back with a bang this June, and fans of the show will finally be able to breathe a sigh of relief.
Esther McVey, who has promised as leader she would "embrace" a no-deal Brexit, said: "The result in Peterborough is the shape of things to come if we don't deliver a clean Brexit on October 31".
Hard-core Brexiteers in the British leadership contest say they would rather take Britain out of the bloc with no deal than countenance a further delay.
FILE - Britain's Secretary of State for Environment, Food and Rural Affairs Michael Gove leaves 10 Downing Street in London, May 22, 2018.
Suspending parliament - officially it would be called proroguing - would render lawmakers powerless and unable to vote to block the government from leaving the European Union on the latest departure deadline of October 31.
May became Britain's second female prime minister in July 2016, after her predecessor David Cameron stepped down in the wake of the European Union referendum.
Leadership candidate Dominic Raab has suggested he'd be willing to suspend Parliament - a process known as prorogation - if legislators looked set to delay or block Brexit.
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Asked how Nigel Farage was feeling after the result, Mr Tice said: "Nigel has gone home downhearted but not surprised as the Labour Party have thrown everything but the kitchen sink at this by-election to get the result they desperately needed, literally dragging people out of their houses tonight to get them to the polling stations".