Offer a prize if your children can go a week without asking you to buy them something.

Pretend that the stress of shopping makes you deaf.

Agree that they can only ask for the same thing three times. If they ask a fourth it means you will never ever get it for them. This has the effect of making sure each time is a really good, reasoned argument for the item in question and not just a whine.

Pester them back! ‘Oh pleeeeease pleeeeeeease buy me some chocolate with your pocket money! ‘

Start singing loudly or dancing every time they ask for something in public, the embarrassment shuts them up immediately.

Start a sticker chart and add one every time they pester you. Every time they reach five, they have to pay a penalty, for instance losing pocket money or doing chores.

If they are over 9 run away from them, down the supermarket aisles. When they find you again explain that this is what will happen every time they ask for something.

Have a pester list. Every time they want something they write it down on the list. Provided they have not whinged and whined for it (in which case it gets removed) the list is used by family and friends to choose Christmas and birthday presents.