Sainsbury, Tesco and Safeway asked a judge to quash planning permission granted by Thurrock council, Essex, to Costco, an American-based company, for a 12,880sq m warehouse with more than 800 parking spaces at the Lakeside Trading Estate.
The three supermarkets claim the council acted unlawfully in treating Costco as a wholesaler rather than a retailer and failing to apply stringent local and national planning policy on retail trade.
They argue that warehouses such as Costco - where fee-paying members can buy cheap food and goods in bulk - are to a significant extent engaged in retail selling.
The supermarkets' counsel, David Pannick QC, said the council failed to have regard to the stated view of the Secretary of State for the Environment that warehouse clubs should be treated as retail.
The hearing, was adjourned until today.