Yes, its Smilax aspera. Unfortunately very difficult if not impossible to root from cuttings. Though a woody climber its a monocotyledon (like Bamboo, Asparagus and Yams) and all the root generating hormones stay down in or near the roots at the point where the stems emerge from the ground. I brought seed back of a North American species (Smilax rotundifolia) several years ago but lost the damn seeds in transit.

Thanks for the info. Do you know if it is possible to root the cuttings here in the UK?

Not sure. Probably best layered so that they are still attached to a plant. Semi ripe cuttings in July might be an option but success will be low and they will be slow to take off.