Thanks for the suggestions so far.
It's a PC - desktop with a separate monitor. I've already tried everything suggested apart from swapping the monitor itself.
I've also pulled apart and reseated all the DC connections from the power supply to the motherboard and any intermediate connections (and wiggled the leads to see it there was a dry joint somewhere).
I've removed, cleaned and re-seated the processor and its heat sink and renewed the heat transfer paste between the two. According to the BIOS, it's not overheating anyway but I wanted to check the connections were good and eliminate that as a possible fault.
The memory sticks (2 x 4GB) have been reseated. The motherboard is a mini PCI form and has integral video and sound cards, so there's nothing to re-seat there. I've run a diagnostic check on the SSD hard drive - perfect result there, no errors showing at all.
The video driver is a possibility I'll look into - it was recently updated to the latest version of Windows 10 (!) but I can't precisely pin the problem to that date event. I have checked to see if it was possible to upgrade (?) to Win 11 but apparently the M/board isn't compatible (I've tried checking and changing the security settings in the BIOS as suggested by Mr. Gates' minions, but that makes no difference).
Maybe it's time for a new motherboard....
Edit: Just confirmed by playing a YouTube video that it's only the picture that fails, the sound continues normally.