Several firms have paused shipments through the route after vessels were attacked by Houthi rebels in Yemen.
It has forced several companies to re-route cargo around Africa’s Cape of Good Hope, adding days to journeys.
But one major shipping firm claimed the disruption will not lead to empty shop shelves.
Houthi militants in Yemen have stepped up attacks on vessels since the start of the Israel-Hamas war in October.
Iran-backed rebels have used drones and rockets to target foreign-owned ships transporting goods through the Bab al-Mandab Strait and the Suez Canal.
They added that the firm was looking for other options to ensure its products would be available to customers.
The alternative shipping route, around the Cape of Good Hope, adds about 3,500 nautical miles to the journey and takes about 10 extra days.
Supply chain research company Project 44 has said items could start to be missing from shelves by February.
Andrew Opie, the British Retail Consortium’s director of food and sustainability, told the BBC the current crisis would not have any effect on the holiday season as those products are already in the UK, but warned: “In the longer term, some goods may take longer to be shipped, as they are routed via longer routes.”
As well as delays to products, longer journeys will increase shipping costs which could impact customers’ prices.
Shipping analysts Xeneta estimate every journey between Asia and Northern Europe could cost an extra $1m (£790,000).
Nils Haupt, head of corporate communications at shipping firm Hapag Lloyd, told the BBC’s Today program that bookings for new freight trips are set to cost more.
However, he added that transport costs were a relatively small part of the overall costs of most products, so he did not expect consumers to see a “huge increase” in prices.
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