There are currently no missing addr:city Post Town values for any objects with DE or NG postcodes https://osm.mathmos.net/addresses/post-towns/
Outside of the centres of post towns I've often added addr:suburb, addr:village and for Wirksworth (addr:city = Matlock) and Castle Donington (addr:city = Derby) addr:town. Am fairly relaxed as long as addr:city is populated. I sometimes add addr:hamlet and have seen addr:locality or addr:suburb used generically 