The Ukip leader told The Andrew Marr Show on BBC One that voters have the chance to make Britain a "self-governing, self-confident" country by supporting the Leave campaign at the forthcoming referendum on the UK's membership of the European Union.
And Farage said he believes a vote to leave the EU will see Cameron replaced in Number 10.
Farage said: "If we win the referendum we have to make sure that a British government carries out the will of the people.
"I have seen referendums all over Europe where the people's voice has been ignored.
"So Ukip being strong and making sure that the Government and the prime minister – which won't be David Cameron in my view – but whoever it is, making sure they do go for Article 50 of the treaty and start the process of political divorce."
Meanwhile, Farage was also asked to set out his vision of a post-Brexit UK.
"Self-governing, self-confident and much more global in outlook," he said.
"We have become too obsessed with Europe. It's an important market place but there is a big world out there."
Farage made the case for increased social mobility as he was asked what sort of state Ukip would deliver if it was in power.
He said: "The big thing I can see is there are 7% of people in this country, people like you and me, whose parents are rich enough to send us to private school and that 7% are now dominating business, politics, the media, even sport and the rest of the population is being left behind.
"I think we need a lot more social mobility in this country. I think much of that comes through the education system."
Farage was also asked how he would feel if Scotland voted to remain in the EU but the rest of the UK voted to leave, prompting the possibility of another Scottish independence referendum.
He said: "This referendum is about whether we want independence so if the UK votes for independence, Nicola Sturgeon is then going to have a referendum against independence and with oil on 37 dollars a barrel? I don't think so.
"It isn't going to happen and if there was a referendum she would lose by a much bigger margin than she did in 2014."