Thanks all, sorry for the confusion, I try and rephrase...
The pickup cover sits flush on the surface of the bass. However in the case of my bass, the strings foul the top of the cover.
Thank you, iiipopes, the problem described is very similar to mine (I didn't find this when browsing).
Initially I considered trying to machine the cover, unfortunately I do not have assess to suitable equipment, or know anyone who does. My solution was to recess the body, so that the cover sits on a shoulder below the surface of the body. Before charging in with a router, I was hoping someone might be able to help with the typical string clearance over the top of the pick-up cover.