Supplies to Shell fuel stations could be disrupted later this month.
Shell fuel is delivered solely in tankers operated by Hoyer UK and Suckling Transport, whose 500 drivers have voted to go on strike over a pay dispute.
The drivers want a 13% pay rise, but have been offered only 6%.
No further talks are planned, but the two sides are expected to go to the conciliation service ACAS in the next few days to try to halt the strike.
Drivers are planning to stop deliveries on June 13-16 and June 20-23.