LONDON – Prime Minister David Cameron on Tuesday accused those backing a British exit from the European Union of lying to voters – and insisted he is not worried that the “remain” side is losing ground in the battle for votes.

British voters are deciding in a referendum June 23 on whether to leave the 28-nation bloc – a move being called a “Brexit.” With polls giving a mixed picture, bookies’ odds on an “out” vote winning have been slashed from about 4-1 to as short as 2-1 in recent days.

“Leave” supporters feel they are gaining momentum with their argument that leaving the bloc – which grants free movement to 500 million Europeans – is the only way to control immigration. They also say Britain will have more money to spend on public services if it stops sending billions a year to the EU.

Cameron, who heads the “remain” campaign, told a hastily convened press conference that anti-EU campaigners were “resorting to total untruths to con people into taking a leap in the dark.”

He said their claims that Britain would suffer few economic ill effects from leaving were contradicted by “every credible economic organization.”

Asked if he was worried his side was losing, Cameron said “not at all.”

“What I’m worried about, what I’m concerned about, is that people are being told things that aren’t correct,” he said.

He said voters had to choose between “credible experts warning about risks to our economic security on one side and a series of assertions that turn out to be completely untrue on the other.”

Douglas Carswell, lawmaker for the anti-EU U.K. Independence Party, said Cameron’s comments showed “the `In’ campaign is in a blind panic.”

But Cameron’s words were backed up by a warning from the head of the World Trade Organization. Director-general Roberto Azevedo said British businesses could have to pay billions in tariffs for years while Britain negotiated new terms with the EU and the 58 countries with which it has free trade agreements now.

“It would cost more for the U.K. to trade with the same markets – therefore damaging the competitiveness of U.K. companies,” Azevedo told a trade symposium in London.

He added “it is impossible to tell how long it may take” for Britain to work out new trade terms within the global trade organization.