I "think" the claude butler urban takes 700c wheels. Standard 26" mtb tyres (or wheels) wont fit. You will need to either fit cyclo-cross tyres or a set of "29ner" MTB tyres.
Cyclo tyres are more or less the same size as your current tyres, there shouldn't be any issues fitting them to your frame/wheels.
29ner tyres are normally much wider (Although they come in a range of sizes/designs). Your wheels should just about be alright but they might be too wide for your frame or fork. You'll need to ask in a bike shop if they'll fit.
It all depends on what you call "off-road". Cyclo-cross tyres are often better in muddy / smooth hardpacked conditions than a MTB tyre. However, they're far from ideal for rocky terrain.