They hope governments will find ways to up supply and ease pricing, perhaps by halting tariffs so that cheap grain can be imported from the Americas.
Starch is used to bond the three layers of corrugated card together to give it strength.
DS Smith has agreements in place to obtain starch and there are no shortages yet. But as prices rise, concerns are growing that shortages could result.
Global food prices hit a new high last week, led by vegetable oil and grain prices as the war in Ukraine disrupted supplies.
The food price index for March from the US Food and Agriculture Organization rose to a third record-high in a row, up 34pc from a year ago.
Russia and Ukraine together grow almost a quarter of the world’s wheat and the conflict has disrupted harvests and planting in Ukraine, the fifth-biggest exporter. Those shortages will start to be felt in the coming year unless new sources are found.
Food-related protests have already erupted in Sri Lanka and last month World Trade Organisation head Ngozi Okonjo-Iweala warned that rioting could take place in poorer countries that import food as prices become unaffordable.
Synthetic starches are available but are more expensive and many mills are set up to use starch from food.
In common with many heavy industries, the paper industry is suffering large rises in raw material costs, including energy, while also attempting to decarbonise.
A months-long strike at pulp and paper mills in Finland owned by UPM has also put pressure on paper supplies. The strike was extended for another two weeks at the end of March.
Asset manager Abrdn was forced to delay a shareholder vote earlier this year because of a paper shortage that held up printing of a million 120-page documents.