Keyboard shortcuts have gone screwy since Mavericks upgrade
Ahhh this is embarrassing. Seems like this is a hardware problem. I tried following the steps Apple support suggested, and when I do the keyboard input identification in System Preferences OSX tells me my keyboard isn't recognised. I've just remembered I scrubbed the keyboard with a cleaner cloth a few weeks ago to try and get rid of the yellow grease it had accumulated - I guess this must've messed it up. Sorry Mavericks! Thanks a lot for your help Asmus!

Lesson: wear gloves when using white keyboard.