Nigel Farage has called for David Cameron to step down and said the UK needs to be led by "a Brexit Prime Minister".
The Ukip leader also called for June 23 to be declared a Bank Holiday, saying that it will "go down in our history as our independence day".
Mr Farage said: "My feeling is the Prime Minister could have risen up to the fray. He chose not to, I think he probably has to go. I think we have to have a Brexit Prime Minister."
Read more: Britain votes to leave European Union despite Scotland wanting to Remain
He suggested that Boris Johnson, Michael Gove or Liam Fox would be potential leadership contenders.
He accused Mr Cameron and Chancellor George Osborne of behaving in an "appalling" way during the campaign.
He said: "The Conservative party has literally split down the middle over this and I know a lot of Conservative MPs I've spoken to who feel that frankly the way he [David Cameron] and [George] Osborne have behaved in this campaign has been appalling.
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"They have stretched the truth, let's be nice, I could use a stronger word."
He said Conservative backbenchers would not want "this man to stay on".
Mr Farage also said that he hoped the win would bring down the entire "failed project" that is the EU.
Mr Farage said old Labour voters had won the election for Leave.
"The election was won in my view in the Midlands and the North and it was the old Labour vote that came to us and we, particularly as a party, campaigned as hard as we could in those areas," he told reporters on College Green in Westminster.
Read more: Alex Salmond raises prospect of new independence vote after UK Brexit split
"There is still a massive disconnect between Westminster, SW1 and real communities."
He said he hoped Brexit would kick start the break up of the EU.
"Eurosceptic parties never talked about leaving the EU, now they are.
"An opinion poll in the Netherlands said that a majority there now want to leave, so we may well be close perhaps to Nexit.
"Similarly in Denmark a majority there are in favour of leaving so we could be quite close to Dexit.
"And I'm told the same may apply to Sweden and perhaps Austria and perhaps even Italy too.
"The EU is failing, the EU is dying, I hope that we've got the first brick out of the wall."
He added: We need the negotiations to start as soon as humanly possible, we need to start thinking globally about our future, and the other thing I think that needs to happen is that June 23 needs to become a national bank holiday and we will call it independence day."
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