Brexit is not that complicated for the average ecommerce retailer.
Large companies and suppliers that import goods may be affected by increases in tariffs. There could be delays in receiving the goods. But this should not affect small to midsize merchants. And most of the problems will likely occur between the U.K. and mainland Europe.
If you are located outside of the E.U. — in the U.S., for instance — then shipping to E.U. countries will remain unchanged. It is also likely that shipping to customers in the U.K. will remain unchanged. The customs declaration will be the same after Brexit. It is possible that delivery to the U.K. will take a bit longer. Likewise, it is possible that your U.K. customer may have to pay a new import duty. And it’s possible that the value-added-tax exclusion on low-cost items will no longer apply.
If you are located outside of the E.U. — in the U.S., for instance — then shipping to E.U. countries will remain unchanged.
All of these possibilities, if realized, would be your customers’ problem unless you pay all import duties, which I do not recommend. (If a U.K.-based customer complains, point out that Brexit is the cause.)
For U.K.-based merchants, it is unlikely that the products that you can and cannot import will change in the short term. Any change will be years down the line. Likewise, the U.K. will probably keep the same standards and testing regimes as the E.U. and will, similarly, continue to recognize equivalent U.S. standards.
Product territories?
What could happen is that manufacturers and distributors are no longer constrained by the U.K. and E.U. belonging to a single market. This may prompt manufacturers and distributors to create territory licenses and limitations as to who can sell in the U.K. and the E.U. This is currently illegal due to the Treaty of Lisbon.
This change could alter the sales terms that ecommerce retailers receive from suppliers. Presumably, this would not happen without warning — until Brexit is confirmed and enacted. (A supplier or manufacturer that plans to do this will likely keep it a secret until then.)
In the best case scenario, even merchants that ship between the U.K. and the E.U. will see no change — no customs forms, no change in allowable products, and no change in standards, quality tests, and safety certificates. In the worst case, however, it will be similar to how U.K. merchants send parcels outside the E.U. — fill in customs declarations and export certificates (as you do now) for all countries.
Value-added tax
The big difference is value-added tax. Currently, if an E.U.-based business sells to an E.U.-based consumer, the business must collect VAT. The U.K. is presently in the E.U.
If the U.K. leaves the E.U. with no deal, then E.U. and U.K. business no longer have to collect VAT for sales to customers in each locale. (For example, retailers in France selling to the U.K. consumers would no longer collect VAT, nor would retailers in the U.K. selling to consumers in France.) Thus, corresponding prices would presumably be lower. The customer may still be charged VAT on the point of import, but it would be levied by the importer and not the retailer.
All of this could slow down postage for shipments between the U.K. and the E.U., after Brexit. It will likely annoy those customers.
Thus if you ship internationally, Brexit will likely mean doing more of what you already do. If your fulfillment software selects and fills in the relevant forms and labels depending on the shipping location, then it will have to be updated to move the U.K. out of the E.U. bubble.
Sales impact
One final consideration is projected sales. It is possible that bad feelings may develop over Brexit. Consumer demand may dip for products sold between the U.K. and the E.U. Scare stories in the media may cause U.K. and E.U. consumers to buy locally rather than internationally. So there is an opportunity to pick up national sales from patriotic consumers.
However, the only certainty with Brexit is its uncertainty. And uncertainty impacts consumer confidence and thus reduces sales.