I contacted Microsoft Support via the chat function and one of their support staff first validated my product key, told me she would assist me free of charge (I have no support contract with them), then remotely took over my laptop and re-produced the same problem. After an hour of trying various ways she could not get the download to start (same error message all the time).
She then said she would escalate the problem to Level 2 support staff, and asked me what time I would be free to take a call back from them the next day.
The next day, at EXACTLY the time I gave them, a guy called back and again took over my laptop remotely. He re-produced the problem, and then entered a different Product Key than my valid one and successfully started the download for me.
I then thanked the guy and said I'd take it from there. Once the download finished, I started the install, successfully entered my own Product Key and all is now fine.
Hats off Microsoft to you and your excellent support procedures and support staff.
10 out of 10, although it does look to me there's a problem in the download logic somewhere, I can't complain at all about the superb support I received to fix the problem.
Happy Bunny!
:)