Thanks again for replies.
Manoli, I've already run Onyx - haven't bought CleanMyMac3 yet as it has varying reviews, but may need to try it.
Pieter, Library is visible, I don't have iPhone backup or Mail or Music files on this startup disc.
Jjj, DaisyDisk indeed gives more detail. The 'Private' folder has 83.9 Gb of files, Spool subfolder 80.5 Gb, then Cups subfolder of same size with multiple 1.8 Gb & smaller files, with names like d00300-001, d00286-001 etc etc. These look like the culprits but no idea what they are or where they come from or whether they can/should be deleted. DaisyDisk has a support facility which I'll contact.
For interest, DaisyDisk scan image is attached, plus scan of Cups subfolder.