Ok, TimeMachine runs from time to time, backups pile up and the disk is filled. So what now? Format it? No! Drop the oldest backup!
echo "first list all existing backups"
echo "pick the one with the oldest date and delete it; put the name in double quotes"
sudo tmutil delete "/Volumes/driveName/Backups.backupdb/Marcels iMac/2015-05-19-110051"
Initial inspiration for the solution was derived from this thread at stackexchange.