One of the many unresolved issues relating to Brexit is the issue of cross-border retailing.
While there are certainly issues relating to online cross-border shopping (e.g., the imposition of VAT, additional charges for checks as well as delays caused by possible border/customs delays), there are certainly plenty of issues relating to cross-border bricks and mortar retailing as well.
The border between Ireland and Northern Ireland ("NI") is a neat case study.
Such has been the significant flow of people over the Irish/NI border that Sainsbury's achieved at one point a small percentage share of the Republic of Ireland grocery market despite not having a store in the Republic (i.e., so many from the Republic shopped in their NI stores that Sainsbury's registered in the Republic's grocery data). Equally one of Asda's smaller stores in NI became significant at a Walmart level for certain products which had high excise duty in the Republic (e.g., wine) because of the volume and value of cross-border shoppers.
What will be the impact of Brexit?
While there is political agreement that there will be no "hard" border, the border will be "harder" than the current near invisible frictionless one. There will be changes but no one can yet identify those changes. Retailers and others in the chain would be wise to contemplate what they might be.
If the UK leaves the customs union and the internal market then some form of border/customs check seem inevitable. The EU cannot leave the back door ajar on the world's largest tariff-free and quota-free market. So even if the UK does not want border controls then they will probably have to be imposed from the EU side. This will add delays, costs and probably remove a number of smaller suppliers who would be deterred from the additional costs and challenges (most likely limiting the growth potential of UK Small and Medium Sized Enterprises). So retailers should examine their supply chains to see how such controls, charges and changes would affect their range and stock.
Even if it is not a "hard" border, it could well be harder/less soft than the current border so some consumers will be less inclined to cross the border. Charges and checks could be a deterrent.
Winston Churchill said in 1949 that when one gets rid of a "free" market, one creates a "black" market. While his words were obviously said in a different context, they are very apt. If there is a wide divergence between prices and taxes between Ireland and Northern Ireland then that "arbitrage" (or more colloquially, "smuggling") opportunity increases. "White Van Man" for both legal and illegal trade could well flourish.
What is unclear is whether how there will be no controls both north/south and east/west (Britain/Northern Ireland) if the UK leaves the internal market and customs union but the Republic remains in (as is almost inevitable). If the flow of trade is smoother north/south then retailers could well find that supply chains in the island of Ireland might be easier to operate than east/west so retail logistics providers would be well advised to consider how this would work in practice.
Brexit is unlikely to increase cross border retail traffic. However, there may be a silver lining to that cloud. Paradoxically, if Brexit has a detrimental effect on the UK economy then Sterling may fall in value versus the euro thereby encouraging some Republic of Ireland shoppers to still to "go North" despite more obstacles. Otherwise the implications might be lower footfall, higher barriers and more complications. But it may be too early to tell given that the outcome of Brexit is unknown even to its most ardent supporters.