OK, I've been sent the following two links about the Seagate FreeAgent
drive, which explain the problems I'm having and a way to solve them.
Now, all I need to do is find a Windows user so I can sort it out :-)

www.theinquirer.net/gb/inquirer/news/2007/12/06/*seagate*-snubs-*linux
*www.theinquirer.net/gb/inquirer/news/2007/12/11/*seagate*-issues-workaround-*li\
nux
*
I've also made some progress with the WD Passport drive. By formatting
it to FAT32 and writing a couple of udev rules, I can get the drive to
work - but ONLY if I sudo into Nautilus. If I try to access the drive
as a standard user, the owner and group are both set to root - even
though I have explicitly set the group to plugdev - and I can't do
anything with the drive, but if I sudo into Nautilus, the group is
suddenly reported, correctly, as plugdev and I can access the drive.