Barnsley chop is the traditional name in United Kingdom. Outside that tradition, butchers carry comparable lamb cuts under different names — sometimes the same anatomical piece, sometimes a close cousin. The alternatives below are grouped by country so you can match what your local butcher actually carries.
Same anatomical cut from the saddle, but Barnsley chop is cut across both loin eyes plus the spinal bone — a single chop spanning both sides of the animal — while a standard loin chop is cut from one side only.
Both are British grill chops; the Barnsley is a double loin chop, so it is leaner and larger than the chump.