The shock defeat for David Cameron's strong recommendation of a Remain vote led to questions about his future as Prime Minister.
Labour said he should "seriously consider his position" if Leave won, while Mr Farage said he should quit "immediately".
Addressing jubilant supporters at the Leave.EU headquarters as the sun rose over London, Mr Farage said: "I now dare to dream that the dawn is coming up on an independent United Kingdom."
Britain has freed itself from Brussels "without a shot being fired", said the Ukip leader, adding: "If the predictions now are right, this will be a victory for real people, a victory for ordinary people, a victory for decent people.
Pro-Leave Tories including Boris Johnson and Michael Gove signed a letter to Mr Cameron urging him to stay on as leader whatever the result of the referendum.
But others in the party raised questions over the PM's future. Long-standing Eurosceptic John Redwood suggested Tories should wait to see if Mr Cameron was willing to "implement the public will" after a Leave vote. Mr Redwood said the PM should bring in talent from the Leave side to build "a new government to bind the country together". And Conservative backbencher Jacob Rees-Mogg said a general election in the autumn was "not impossible".
Influential backbencher David Davis said the Prime Minister could stay on for a "couple of years" but should put someone else in charge of negotiations on a new relationship with the EU.
Shadow chancellor John McDonnell said the Bank of England may have to intervene to shore up the currency. Mr Cameron would now be "a hostage" to his pro-Brexit MPs, who will make sure they seize "key positions", he said.
Senior Labour backbencher and former Europe minister Keith Vaz said the EU should call an emergency summit to deal with the aftermath of the vote, which he described as "a crushing, crushing decision ... a terrible day for Britain and a terrible day for Europe".
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereLast Updated:
Report this comment Cancel