Thanks all for all the excellent advice.
Just to let you know what happened...
I suggested two options:
1. That he could choose a Toshiba authorised repairer from their website (with prior agreement with myself), return the laptop to me, we get it inspected as agreed with him paying their charges. If & only if they found the fault he described I would refund him in full.
2. As a gesture of goodwill I offered £20, which (not surprisingly with hindsight!) he took.
Maybe I won't be so nice next time?