What you're seeing is the Resource Fork of the file. The FAT on Windows doesn't understand it and it shows as this apparent second file.
Lists many of the apps and utilities that you can use to strip these from the files.
Thanks for the swift reply Terence.
Based on your post I've done a bit more digging. I gather resource forks are also known as DS Store files and that I need to delete them to solve my problem.
However I've now downloaded a number of freeware apps and tried deleting the relevant DS files, but still they show when I put my USB Flash Drive into the USB port on my TV.
I've tried using Onyx, Cocktail and DSWipe and all seem to show that they've successfully deleted the files, but when I plug the flash disc into my TV they're still there. It's as if OS-X automatically rebuilds new DS Store files the moment the old ones are deleted.
What am I doing wrong?