Thanks Daisy and mcvansoest. It certainly looks like an Echinopsis.
I don't know if it is 'Big Bertha', as I've never seen it produce flowers anywhere other than the very top at what I assume is the growth point (never from the sides).
As it is at my parents', I can't give you exact measurements, but here is an older photo my mum sent me:
I have not seen it get taller than about 12" (perhaps 18" on rare occasion) and is around 3 to 4" across.
