Wales and the majority of England outside London voted in large numbers for Brexit.
Labour's Shadow chancellor John McDonnell said the Bank of England may have to intervene to shore up the pound, which lost 3% within moments of the first result showing a strong result for Leave in Sunderland and fell as much as 6.5% against the euro.
UKIP leader Nigel Farage - who has campaigned for the past 20 years for Britain to leave the EU - told cheering supporters "this will be a victory for ordinary people, for decent people".
Mr Farage - who predicted a Remain win at the start of the night after polls suggested that would happen - said Thursday 23 June would "go down in history as our independence day".
He called on Prime Minister David Cameron, who called the referendum but campaigned passionately for a Remain vote, to quit "immediately".