There's an advert in today's Telegraph from the airport authority showing a comparison with high street prices and how much you can save at Heathrow.
I remember back in the 1990s they had to run an advertising campaign after being caught selling "Duty Free" whisky for more than it cost in a supermarket.
Back in those days TV and newspapers were the main source of news, these days with social media and stories going viral everybody knows within a day or two.
With VAT at 20% we're not talking about rounding up a few pennies. Many shops in London have the tax free for tourists scheme and if your spending passes the threshold you can claim back the tax less an admin charge. You may need to reduce the number of shops you purchase from to keep individual receipts high enough and allow extra time at the airport, but you can shop at your leisure and have a far greater selection.