Big pharmaceutical firms like Pfizer Inc. and GlaxoSmithKline PLC are stockpiling medicine, on orders from the British government, just in case of long delays at the border. Cadbury maker Mondelez International Inc. is boosting supplies of chocolate and other ingredients for the same reason. Airbus SE, the European plane maker, is asking suppliers to keep extra parts — potentially worth billions of dollars — on hand ahead of the March separation.

On Tuesday, BMW AG said it was moving up its annual weekslong maintenance shutdown at a plant in Oxford, England, to fall right after Britain’s planned departure. It said that will better protect it from any supply-chain disruptions that might stem from a disorderly breakup.

Britons voted to leave the EU in 2016. The deadline to do so: 11 p.m. local time on March 29. That is now just a little more than six months away, but London and Brussels have failed so far to agree on a deal outlining the terms of the U.K.’s exit.

Companies with business on both sides of the English Channel are grappling with many big, unanswered questions — like whether, or how, goods will be inspected along Britain’s now-seamless border with Europe.

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