Mr Rees-Mogg was appearing at a Bruges Group event highlighting the impact of the European Arrest Warrant on Britain’s justice system alongside Nigel Farage.
Commenting on the claims against the Prime Minister, the Ukip leader said: “I think increasingly in this referendum campaign he’s looking like ‘Dishonest Dave’.
“He ruled nothing out in terms of how the renegotiation went, then three months later he tells us that if we leave it will cause World War Three.
“He clearly has been less than honest with virtually everybody including the House of Commons.”
Out on the Brexit campaign trail with the Vote Leave group, ex-London mayor Boris Johnson said: “This is the biggest stitch up since the Bayeux Tapestry.
“It stinks to high heaven. FTSE 100 chiefs are seeing their pay packets soar while uncontrolled immigration is forcing down wages for British workers.
“Now we learn that some fat cats have been secretly agreeing to campaign for Remain while angling for lavish Government contracts.
“It makes us look like a banana republic. And it is also now beyond doubt that the so-called renegotiation was a fiction designed to bamboozle the public.
“It was a meaningless mime, a ritual, a kabuki drama in which the outcome was utterly preordained. This is not the far-reaching and fundamental reform we were promised.
‘The only safe way to take back control of our borders and our democracy is to Vote Leave on June 23.”