After much experimentation I've found a way of fixing the problem.
I didn't want to risk messing up my game so I started a new game on another Xbox. When I eventually got to see the World Map it was, as I thought, displaying correctly. I then looked at the X:\drive where the constantly being updated Morrowind game files, including the map, are held.
Immediately I noticed that there was an extra file: "Full Map" that is missing from the X:\ drive on my prime Xbox. So I decided the thing to do was to copy that file to the prime Xbox's X:\ drive.
Easier said than done. Copying it to an official memory card or a USB flash drive proved impossible despite there being plenty of room (2MB for a 774kB file). It simply refused to copy giving me an error 183 message every time.
I tried to copy the other map file there too - same problem. But two other files copied without any trouble. Never had anything like that happen with a Xbox memory card. Any explanation appreciated.
Then I tried FTPing between the Xboxes but the problem there was the X:\drive refused to be displayed, maybe because I'd deleted its contents in a previous attempted solution. I couldn't be bothered to re-load the game to create new X:\ drive files again. So, finally, I went the whole hog and using CoreFTP LE FTPed the entire new game X:\ drive contents to my laptop and then from there FTPed to the prime Xbox.
Worked perfectly and when I booted Morrowind and loaded from my latest save the World Map was displaying correctly once again. Yay!
Only problem is that the only locations visited/referred to immediately after starting a new game ie. Seyda Neen and Balmora area are displayed on the World Map. Didn't check the Local Map but I wouldn't be surprised if that was now mostly blank too.
Whether the game will update the dozens of places I've been when (and if) I revisit them and whether this will cause the same World Map issue to recur only time will tell.