I've worked it out now, partially due to @Jacobm001's answer - thanks!
I have /mnt/video mounted to an NFS share on my NAS. I have a cron job which automatically downloads (large) videos and places them in this share.
When I ran the
sudo du -h / | sort -h -r | head -n 10 command, it listed folders on the NAS (subfolders of /mnt/video, as far as the Pi is concerned), so I did
sudo umount /mnt/video before I ran
Second time around, there was still a huge folder within /mnt/video.
It seems that at some point, the share wasn't mounted when the cron job ran, and it filled the local disk (i.e. the SD card) at /mnt/video until it ran out of space.
When the share was subsequently mounted, the contents of the NAS were shown (as expected), which was why I couldn't work out where the space had gone.
With the share unmounted, I was to copy the files from the Pi to the NAS (using
scp) then delete them from the Pi, so now I've got my free space back:
pi@raspberrypi1 ~ $ df -h
Filesystem Size Used Avail Use% Mounted on
/dev/root 6.3G 2.5G 3.4G 43% /
devtmpfs 459M 0 459M 0% /dev
tmpfs 93M 272K 93M 1% /run
tmpfs 5.0M 0 5.0M 0% /run/lock
tmpfs 186M 0 186M 0% /run/shm
/dev/mmcblk0p5 60M 20M 41M 33% /boot
192.168.2.50:/volume1/video 17T 13T 3.9T 77% /mnt/video