I don’t have a Slough car but have just had to attend to my flat boot Normale’s wipers. I imagine you have the later style of wipers with. Lucas motor operating a cable-type rack common to all sorts of British cars of the 50s and 60s. If you are sure there is +12 volts getting to the motor, the next thing to be sure of is the earth. That’s what stopped mine. If that’s ok then either your motor brushes have a problem or there’s a problem in the park switch in the motor. I suppose it is also possible that the rack has got jammed, maybe in the wheel-box that drives one of the wiper spindles. From my memory of fiddling with my Triumph’s wiper motor, I think taking the cover off the gear that drives the rack is quite easy and exposed the gear that drives the rack. It also exposed the cam that drives the self park switch. I’d go there before having a look at the brushes. Not sure if this helps.
Chris