Ukip's deputy leader Paul Nuttall has said he won't be bidding to replace Nigel Farage as the head of the party and also plans to step down from his current position.
Mr Nuttall, who was viewed as one of the favourites to succeed Mr Farage, said he had achieved his objectives following the Brexit vote.
I have been at the forefront of the campaign to leave the European Union for a decade now, and I believe I can step aside with my objective achieved and my head held high.
The North West England MEP said he would keep his seat in the European Parliament to "hold the Government's feet to the fire" during the talks on leaving the EU.
Video report by ITV News Political Correspondent Libby Wiener
Nigel Farage declared "job done!" as he stepped down as Ukip leader today.
"I now feel that I've done my bit. I couldn't possibly achieve more than I managed to get in that referendum," he said.
The pro-Brexit campaigner is still an MEP but insisted he would not be returning to politics again.
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Nigel Farage has been told to give up his seat as a Member of the European Parliament following his resignation as Ukip leader.
Liberal Democrat foreign affairs spokesman Tom Brake said: "Nigel Farage has spent years attacking the so-called Brussels gravy train while doing his best to cash in on EU taxpayer-funded expenses.
"This rank hypocrisy has to end. It's high time he did the honourable thing and resigned as an MEP and stopped milking taxpayers to push his divisive agenda."
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Neil Hamilton, the leader of Ukip in the Welsh Assembly, has said Nigel Farage should get a peerage for his "significant achievements".
In a statement, he admitted the pair "have not always seen eye to eye" but Farage is "one of the great figures in British politics today".
It is well known that I have not always seen eye to eye with Nigel, but I salute his very significant achievements.
UKIP has a massive continuing role to play in British politics and, under a new leader, we will reach out to an even wider constituency.
Nigel Farage deserves the thanks of every Brexiteer. There would have been no referendum without him. He is a controversial figure but, like him or loathe him, he is a dynamic force and one of the great figures in British politics today. He clearly has much still to offer in the continuing campaign for an independent Britain. He should be given a peerage.
Douglas Carswell has told ITV News he will not stand to replace Nigel Farage as Ukip leader.
Asked whether he wanted to succeed Farage, Ukip's only member of Parliament replied: "Absolutely not - I couldn't possibly be a constituency MP, represent Ukip in the House of Commons, be a dad and lead a party."
Carswell, who has been locked in a feud with Farage, earlier tweeted a smiling emoji as news of the leader's decision to quit emerged.
Carswell admitted he and Farage had suffered "profound differences in opinion" over how the party should operate.
But he paid tribute to his former boss' role in convincing Britain to vote to leave the EU.
"For 20 years, Nigel stood at times almost alone in pushing for this referendum...we got the referendum and we won. Nigel played a key role in that and I think we should pay tribute to him."
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Ed Miliband has said he is "not sorry to see Nigel Farage leaving the political scene".
The former Labour leader said Ukip had a record of "stirring up division" under Farage's leadership.
"I'm not sorry to see Nigel Farage leaving the political scene," he told the BBC's Victoria Derbyshire show.
Nigel Farage has refused to say who he believes should replace him as leader of the UK Independence Party.
When asked by ITV News Political Correspondent Carl Dinnen on who would be best suited to replace him, Mr Farage said: "I'm going to keep very quiet on that, and may the best man or the best woman win."
Farage stood down on Monday morning, saying he "never wanted to be a career politician".