Thank you both artie505 and joemikeb for your advice which has narrowed the solution space to zero and I now know that my new iPhone is in transit.
I had previously allowed a substantial timeout period for both Safari and Firefox. Logging into the guest user account didn't fix it. However the process of logging back into my own account *has* solved the problem and Apple web pages now load satisfactorily. Logging out and back in seems like a good troubleshooting tool to add to the arsenal and a lot quicker than a restart
It's still a mystery to me why, whatever the issue was, it only affected Apple sites. I don't want to think about it!
