Final update: Success at last!
After a truly awe-inspiring amount of procrastination and obfuscation, it finally occurred to Dell that I was going to keep yapping at their heels until I got some satisfaction. They have finally agreed to a "once-only offer" to send a technician out and replace the screen free of charge.
I found it odd that after all the emails exchanged, diverted, bounced and referred, the offer was finally made over the phone. Not that I'm the suspicious type of course, but I then sent them an email providing my daughter's address and thanking them for the confirmed offer to replace the screen free of charge.
Believe me, patience is required, but thanks to
matelot's advice and
Bo Nalls' link, a happy outcome has been achieved. The consumer can win in the end; you bloody beauty!