Cookery Programme is more for teaching people how to cook.
Food and Drink Show is more related to introducing the latest restaurants, food and fancy drinks to the public.
So depending on what you want/mean, choose the most suitable one.
We classify these types of show either cooking show or cookery show, even they are not ONLY show you how to cook, in US most of the famous chef has their own show, not only teach you how to cook, almost everything about food, china, cooking utensils, dining room decor .....