Britain leaving the EU would cause a profound economic shock according to Chancellor George Osborne.
He said it was the “very worst time” for Britain to take such an “enormous economic gamble”.
But ex-Conservative leader Michael Howard disagreed, saying the UK should have the “self-belief” to go its own way.
Lord Howard argued the EU was “outdated, flawed and failing” and an Out vote would force its leaders to think again.
The prime minister’s official spokesman said Mr Cameron had “huge respect for Michael Howard but on this issue they disagree”.
On 23rd June, the UK will hold a referendum to decide whether to stay or leave the EU (a so-called “Brexit”).
Lord Howard said it was not the PM’s fault he had not been able to secure “fundamental and far-reaching reform” of the EU.
In the past, he had been a close political ally of Mr Osborne and Mr Cameron, and led the Tories between 2003 and 2005.
He blamed EU leaders for imposing a “rigid straitjacket of uniformity” across the continent.
He argued, as the world’s fifth largest economy, the UK would prosper outside the European Union; “the Germans would still want to carry on selling us their BMWs and the French would still want to carry on selling us their wine”.
Subedited by Pete Adams