Thanks for the very helpful reply.
I found the library folder that the IDE was using and the EEPROM.h was different from the one pointed to by the make file. (I hadn't found it originally as it is in a hidden folder.)
I'm ashamed to say that I used a brute force method to fix my arduino-mk make, by coping the EEPROM library folder from the complicated path used by the IDE to the path looked for in the make file /usr/....
I understand that this is a kludge because you said that it was hardware specific; I'll cross that bridge if I ever come to it...
I understand that in the future you may say "I told you so!"
As an aside, I really appreciate that you took the time to answer my actual question and didn't tell me that I aught to be doing something different. That happens a lot on the FaceBook based pages... (:-X )
Best regards
Gareth