Well... it gradually got worse, and I couldn't access my node-RED editor 'flows' at all, from any browser, even a mobile browser.
However, after delving through the Cloudflare menus, I found a setting - 'Browser Cache Expiration' which was set to 8 days, and had been set that way for over 2 years without any problems whatsoever.
Changing this setting to 'Respect Existing Headers' and clearing the Cloudflare cache, immediately enabled the flows to load OK across all browsers.
I reversed the process to check a further twice, and on each occasion that the setting was other than 'Respect Existing Headers', the flow's refused to load.
Sorted!