Update 11.30am: Nigel Farage added that he would keep up the pressure in Brussels as a member of the European Parliament.
"There will be a strong Ukip voice in that parliament during the negotiations.
"If we see significant backsliding or weakness or, frankly, appeasement from the British government we will certainly say so."
He indicated that Ukip - and potentially he himself - should play a part in the Brexit talks.
"I have no idea whether they want to ask me or anybody else in Ukip to be part of this. But we do actually as a party have some good knowledge of how Brussels works and we have got some pretty senior business figures amongst our supporters."
He added: "I'm not putting myself forward. I did spend 20 years in business and I have spent a lot of time in Brussels, I might have something to give if they want it. If they don't, that's fine."
Earlier Nigel Farage has announced he is stepping down as leader of Ukip, saying "I've done my bit."
He said of his decision: "I won’t be changing my mind again, I can promise you" in reference to his previous resignation, which he reversed to run a campaign for Brexit.
"What I said during the referendum campaign is I want my country back. What I’m saying today is I want my life back. And it begins right now," he said.
He said now that Brexit had been achieved, he felt it was time to step down, adding: "I'm not a career politician."
He said he did not believe there would be a general election in the UK this autumn, despite the Brexit result and despite leadership struggles in both the Conservatives and in the Labour party.
Of Brexit, he said: "There would not have been an EU referendum without Ukip."
Mr Farage said he would see out the remaining two years of his term as Member of the European Parliament (MEP) for the South East of England.
"We need to stand up for ourselves" in the upcoming Brexit negotitaions, he said, warning against "appeasement".
Mr Farage, 52, has had two stints as leader of the Eurosceptic party since 2006, and announced he was quitting the post after failing to win a Commons seat in the 2015 general election, only to change his mind days later.
His statement, released by Ukip, said: "The victory for the Leave side in the referendum means that my political ambition has been achieved. I came into this struggle from business because I wanted us to be a self-governing nation, not to become a career politician.
"Ukip is in a good position and will continue, with my full support, to attract a significant vote. Whilst we will now leave the European Union, the terms of our withdrawal are unclear. If there is too much backsliding by the Government and with the Labour Party detached from many of its voters then Ukip's best days may be yet to come".