Regarding the google rankings, I don't see how you can divorce the "Cork City" hits from the "Cork County" hits.  Which is a very relevant distinction.  On whatlinkshere, there are 1100 inlinks to city and 800 to county; pretty close.  If there were no other convention, then Cork would already be a disambiguation page even without cork (material) to contend with.  However, the overriding convention appears to be (Wikipedia talk:Manual of Style (Ireland-related articles)#Disambiguation of locations in Ireland):
Where a town and county have the same name, the county article should be named as County Countyname, and the town should be located at County/townname (if no further disambiguation is needed). For example, Sligo and County Sligo.
It's only a talk-page suggestion, but absent anything stronger it's unexceptionable.  However, throw cork (material) back into the mix and it's clear that it's not a contest between material and city; it's a contest between material, city and county.  To me is a clear case where disambiguation is required, as the only reason city is preferred to county is a very obscure and largely arbiitratry Wikipedia convention.