Ok, I've now cracked the problem of File History not recognising my external USB expansion drive, even though the drive had worked initially and it was behaving normally in File Explorer. Here's how I did it - it worked for me on my PC - maybe it will work for others.
- Open File History and click Select Drive. Select a different drive than the one that is failing to be recognised. (If necessary add an extra internal HDD to your PC. If you have a laptop you could try adding an additional external USB drive to a different USB port - I haven't tried this.) Proceed to set up File History on the new drive. Then turn File History off on the new drive so that a whole lot of your files are not transferred there.
- Go to the external USB drive that wasn't being recognised, find the File History folder and rename it to "File History.old" or delete it.
- Go to your C:\Users\your user folder\AppData\Local\Microsoft\Windows, find the File History folder and rename it "File History.old" or delete it.
- Re-open File History, click Select drive and select the original USB drive that was not being recognised. The drive should now set up normally and start operating.
- Delete the File History folder on the spare drive used in procedure 1. above.
The above process is relevant to situations where people may have altered drive letters by adding or removing drives or moving the system between drives and because of this the File History configuration files are pointing at the wrong drive.