UPDATE!!!!!!
Yesterday, I was perusing pickles at Sainsbury's. I generally get whatever I can stomach because Adam likes having them around, regardless.
I looked at the own brand ones. One was labelled as 'in sweet vinegar' and the other was labelled as 'in vinegar'.
Bought the plain vinegar kind (79p a jar) and they are good. VERY sour. (Though, really, in the states, they'd be a half-sour, I think.)
I've found a passable pickle!