Voters in five out of the six areas in Cumbria have come out in favour of leaving the European Union.
Almost 285,000 people voted in the county, with South Lakeland the only area to vote for the Remain campaign.
Allerdale, Carlisle, Eden, Copeland and Barrow-in-Furness voted in favour of leaving.
Lib Dem leader Tim Farron, who is the MP for Westmorland and Lonsdale, said he was "gutted and heartbroken" by the result.
Copeland had the highest turnout in favour of leaving the EU with 62%. In South Lakeland 53% of voters backed the Remain campaign.
James Airey, the leader of the Conservative group on Cumbria County Council, backed a leave vote.
He said: "It had become clear to me talking to people that this was the way the vote would go. The EU has become a monster in recent years and undemocratic in the way that it is run.
"This is a vote against the establishment."
He also urged voters not to worry about the drop in the value of the pound. "The drop in value is a knee-jerk reaction - it will level out." he said.
Mr Farron has accused Labour leader Jeremy Corbyn of being "spineless" and said the prime minister had let people down "massively".
"This self-inflicted wound will be Cameron's legacy," he said. "This is his failing. And when the call went out to Jeremy Corbyn, he refused to answer.
"The prime minister must now act quickly to steady the economy, reassure the markets, and immediately set a new course."
Voter Bob Maltman, who runs the Bob In cafe in Barrow, backed the Leave campaign.
He said: "There's too much legislation coming from Brussels." Daphne Quinn, who also runs the cafe, was in favour of remaining in the EU.
She said: "Economically, for such a small island the government was doing a fantastic job - keeping the status quo was important, now we are going into the unknown."
John Woodcock, Labour MP for Barrow tweeted: "Listening to people saying Labour voters decided to opt for Leave as message to Tory Govt. If that's our conclusion then Labour is toast."