It's bad luck that the belt broke after that period, but I think you should simply accept that it is bad luck. Your consumer entitlements do not last forever.
Write to head office customer services department, the worst that can happen is that they say no to a contribution to the repair. Put on the compliments head, "wonderful car", "exceptional vale", "highly reliable", "great warranty", "shock horror that this problem arose so close to end of warranty", etc. - you know the kind of BS.
Definitely worth asking. I had a FOC repair to a dodgy horn done (main dealer) on a second hand 6 year old car that was just out of it's one year warranty.
Check honest john etc - if it's a common fault or one which the subject of a previous recall, the head office may look on your request a bit more kindly
Please do Daddy, I just believe that dealers will make excuses not to have to do the work if necessary, and will want to charge instead. Being realistic thats all! Would love to know the outcome though, please do keep us informed!