Steve Hilton, former strategy director for David Cameron, says that his old boss was told EU free movement rules meant he could not hit his net migration target.
Richard Tice, co-founder of Leave.EU told Sam Delaney that this didn't reflect well on the PM.
"Anybody who has any knowledge of this debate has known for years that being in the European Union means free movement of people, and the Prime Minister must have known," he said.
"If he didn't, then frankly he's just not being very bright. It would be impossible to meet his claim.
"He's got a track record of saying one thing, in the full knowledge that he can't or won't deliver. When's he going to stop fibbing to the British people?"
There has also been much discussion over whether Turkey will join the EU – and Tice worries about Cameron's decision on this.
"The Prime Minister was asked three times on Sunday night, would he exercise a veto, and three times he didn't confirm it."
He points out many experts who have warned of economic problems if we choose to leave the EU, but believes they may not be right.
"If it's that cataclysmic, the prime minister should not have called it in the first place. A lot of those experts said that we should join the euro and thank God for Gordon Brown, we didn’t. The experts often get it wrong."
Tice predicts a victory for Leave.
"People know that they are being fibbed to and bullied and threatened, with all these scare stories form the treasury and the IMF and the CBI. All these people who failed in their predictions before.
"People have got to go with their gut and I think people that people will say 'I think we are big enough to be a self governing nation in control of our laws and borders and we should vote to leave'."