It now seems that this show is going to air tomorrow. From the Burleigh website:
Burleigh are featuring in an item about the Willow pattern on BBC's The One Show. It will feature the Factory and show how our unique transfer-printed products are made. A couple who have collected the Willow pattern for over 30 years will talk about their large and interesting collection.

This will be shown on BBC 1, 28th September 2010 and starts at 7pm.
We hope you can tune in and enjoy it!