Nigel Farage's new Brexit Party failed to win its first seat in Britain's parliament.

Anti-EU populist Nigel Farage's new Brexit Party failed to win its first seat in Britain's parliament as it lost out to the main opposition Labour Party in a crunch by-election, results on Friday showed.

The poll in the eastern English city of Peterborough was triggered after the sitting MP, Fiona Onasanya, was dumped by voters after being jailed for lying over a speeding offence.

The Brexit Party's candidate Mike Greene, a local entrepreneur, came in second with nearly 29 percent of the vote, behind Labour's Lisa Forbes, who won around 31 percent. The ruling Conservatives came third with 21 percent, while the Liberal Democrats won 12 percent.

Friday's result is a setback for the Brexit Party -- founded by eurosceptic figurehead Farage only a few months ago -- which came out on top in the European elections in May with 31.6 percent of votes cast.

It had been seeking to capitalise on that momentum as well as voter disillusionment with the main Conservative and Labour parties, who have historically shared the Peterborough seat.

Prime Minister Theresa May is stepping down after delaying Brexit twice as she tried and failed to get her EU divorce deal through parliament.

Farage, who has called for Britain to leave the bloc without a deal, said last weekend while campaigning he saw the by-election as "the opportunity for the next chapter in this great story".