Speaking to BBC Radio 5 Live, he praised the former leader, who “achieved a lot”, but said the time was right for him to step down.
When asked if Ukip would be “better off” with Mr Farage leading, Mr Reeve replied: “Definitely not.”
Peter Reeve defended Paul Nuttall's leadership on Radio 5 Live
Is he the man to take us to the next stage to stand up for the next campaigns? I think Paul Nuttall’s much better qualified
After being probed further, he continued: “Nigel is a great guy and he has a huge following around the country – around the world some would say.
“And he is a man who you have to accept that took a party from nowhere in the 90s to beating the Government in continuous European elections to winning a Brexit campaign that nobody said could be done.
“Even the Prime Minister who called it didn’t actually think it was going to happen – that’s why he called it. That’s why the civil service went into paralysis for three months.
Nigel Farage in pictures Mon, April 3, 2017
Nigel Farage is a British politician who has been the leader of the UK Independence Party since October 2016.
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Nigel Farage in pictures
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Paul Nuttall was hailed as being "better qualified" to take the party forward
“So he’s achieved a lot, but is he the man to take us to the next stage to stand up for the next campaigns? I think Paul Nuttall’s much better qualified.”
He said the party intended to turn its attention to protecting the countryside from development and limiting foreign aid while continuing to promote tighter controls on immigration.
Mr Reeve said: “The mission of Ukip is to stand up against the establishment for ordinary people and that’s as relevant in town halls up and down country and Westminster as it was in the mission [to leave the EU]
“We’ve started to put right what everyone said couldn’t be done and that’s leaving the EU, we intend to do the same in Westminster and in town halls, that’s what Ukip’s all about.
“It’s unprecedented in British history that a party who wasn’t even represented by more than one member in Parliament actually led and is still leading the national agenda. That’s the phenomenon of Ukip.”