I've got a Jessops 360AFD flash and I'm looking for a diffuser for it (the original one is broken). I have been led to believe it is the same as a Pentax AF360.
Is this the case? Or have I had misinformation?
No. The Jessops 360AFD is almost certainly a relabeled version of the Tumax DPT386AFZ. This flash is made by Icorp Development Ltd., a Hong Kong company which makes low-cost reverse-engineered dedicated system flashes sold under the Tumax brand and also as what they call "private label" products.
Other versions of this flash, or other models from Tumax, are sold under brands like Digital Concepts, Vivitar (a brand unrelated to the old-school Vivitar company), Bell and Howell, Bower, and so on. Various versions of this flash often claim slightly different guide numbers, but 36m is on the low side. Presumably a company can order them that way to cut costs — or it's possible that it's just older version than currently offered.
Reviews are mixed; some people are happy with the results for the lower price than the camera-system brands or from bigger third-party flash companies, while others have bad experiences with quality and support. Support is a big deal: in the US, the companies selling these models are basically cheap-chinese-electronics-importers, not camera companies, and customer support is not in their business model. I don't know if that's the case with Jessops. Have you contacted them about the broken diffuser?
Their guide number and zoom range are the same, but they are certainly not the same model. For example, the Jessops has ability swivel and is available for multiple brands, while Pentax is a dedicated P-TTL capable flash without swivel.
As reported, head size of the Pentax is 2 9/16" wide by 1 5/8" high (65 x 41 mm). Compare that with your Jessops to see if its diffuser might fit.