However, passengers may be relieved to hear they are unlikely to be forced to walk through the new stores to leave the terminal, in contrast to being channelled through duty free shops to reach departure gates.
Edinburgh, Glasgow and Aberdeen airports are lobbying Chancellor Rishi Sunak to permit on-arrival duty free sales after their passenger numbers fell by as much as 98 per cent because of lockdown travel restrictions.
They have all cut staff, with Edinburgh Airport, normally Scotland’s busiest, shedding one third of its 750-strong workforce.
The airports’ duty free shops offer alcohol and perfume at around 20 per cent less than high-street prices for passengers leaving the UK.
It is expected similar discounts would apply if on-arrival shops were introduced for passengers flying in from outside the UK.
The stores give a proportion of their sales to the airports rather than pay rent.
Such shops operate in other non-European Union countries such as Norway, Iceland, Switzerland, and elsewhere such as the Middle East, Asia and Australia.
AGS Airports, which runs Aberdeen, Glasgow and Southampton said it had written to Mr Sunak and local MPs “to highlight this as a possible jobs boost and revenue source”.
Its spokesperson said: “The introduction of arrivals duty-free stores would help to offset some of losses our airports have suffered as a result of the devastating effects of Covid-19, and we have made this clear to the UK Government.
“This easy-to-implement, cost-neutral policy would also provide support for regional airports, deliver much-needed new jobs and be of great benefit to our passengers.”
A spokesman for Edinburgh Airport said: “Duty free on-arrivals stores have been successfully deployed around the world.
“Their introduction in Scotland would significantly help our travel sector recover after one of the most damaging periods it has ever faced.
“These stores would create jobs, directly at the airport and indirectly in supply chains, increase revenue and showcase the provenance of top-quality Scottish products like malt whisky.
"We encourage the UK Government to look carefully at these proposals and act to support the travel industry’s recovery.”
However, the UK Government suggested it remained to be persuaded of the merits of such shops, and pointed out that duty free now applied to those travelling to EU countries.
The Treasury said duty free on-arrival “conflicts with international principles of taxation which suggest that goods should be taxed in the country where they are consumed”.
"The introduction of such a scheme could also undermine the UK high street and public health objectives.”
A spokesperson said: “At the start of the year, we gave British airports a boost by changing the rules for the first time in 20 years so that people travelling to the EU can buy beers, wines and spirits duty free.
“We’ve supported the travel sector since the start of the crisis and will continue to do so as we recover.”
The Treasury said the aviation sector could draw on an “unprecedented package of economic measures” which included loan guarantee and job retention schemes, and tax and VAT deferrals.