It was never an issue until recently because all UK airports had separate departure lounges for domestic and for international passengers. VAT was due on sales from the first but not the second.
When combined departure lounges were finally allowed (and the taxman was long against them) it was agreed that VAT due would be "proportionalised" dependent on the sales split made, and operators were required to keep records, which is what this is all about.
Prices, unlike in the USA, do not explicitly show the tax element, if a suitcase is GBP120 then VAT is due of £20 for a domestic passenger or none for an international departing passenger. If the records show that 25% of the suitcases were bought by domestic passengers then the taxman just expects £5 for everything. It's not done down to the transaction level, but gives a good enough calculation which is easy to administer.
Airport departure shops (I refuse to call them "duty free") have long priced way different to mainstream retail, and are a significant revenue stream for operators. It may be that suitcase retails on the High Street for £70, including VAT. Some operators claim boldly that their pricing is never more than mainstream retail. This is achieved by having manufacturers produce for them (slightly) different products, different sizes, etc, which are never sold through outside retailers.
(For flights to JER I never could figure out, though.)
Jersey is not part of the EU and does not have VAT, therefore treated as international.
I understand that airside restaurants are expected to pay VAT (consumed in the UK). Packaged sandwiches sold by Boots etc do not have VAT due, being "food". Chocolate does have VAT due.