Cullum, who is a similar height, hair colour and shape to the hellraiser, is often stopped by confused rock fans on the street - but is flattered by the attention.
The 27-year-old says, "This lovely lady came up to me in (furniture store) Ikea asking for an autograph. Sadly she thought I was Pete Doherty.
"I didn't mind though. The only time I get hacked off is when someone wants to take a photograph of me when I've just stepped off a long haul flight and I'm knackered."