Hi there GrannyJKH,
You've taken some great steps already with Safari. Does quitting Safari, restarting your iMac, and trying to visit those websites to view those images help? We're asking this as both quitting and restarting can refresh the macOS and apps, which may help resolve issues. If needed, the articles below show how:
Also, another thing you can try to help isolate this issue is to log into your iMac in a temporary new user: Set up users, guests, and groups on Mac - Apple Support A new user doesn't have custom or changed settings, and can help determine possible next steps by isolating this further. Does the same issue happen in a new user as well?
Let us know how those steps go or if you've already tried those.
Take care.