Thanks for these replies. The replace C: with D: method lost the categorisation totally. I tried it twice.
I tried some of the suggestions on the Wiki page but could not find the right combination - something always went wrong such as the files from subfolders being put into the same base folder.
However I have now discovered that the Drag and Drop method (in Drives and Devices) will work properly providing that I adjust the autoimport settings to include the new location. Maybe the other methods would have worked if I'd also adjusted the autoimport settings too. Maybe a warning to do that should be added to the Wiki and other instructions.
If I might also comment that while the "Library Tools / Rename Move and Copy Files" dialog is obviously powerful and flexible, it is hard for a novice occasional user to understand exactly how to get the result that they might require. The Help button certainly gives some help, but did not, for me, give the level of detail that I needed. A "What Do You Want to Do?" section, with exact steps for getting just that result (such as adjusting autoimport) would have been really helpful.
Thanks again.