I think Parasene is the brand name, paraffin is the fuel. We had one, still got it in fact, but it was dangerous because it repeatedly fell over, so choose your model carefully.
Great news you're getting on with the allotment. Once you really get going you'll wonder how you ever lived without one. We had allotments for years before we eventually moved up to the smallholding, but I still miss mine sometimes, especially the camaraderie, and others to discuss growing with
But of course I've got TAS now