The food retailer will not accept any new orders at its Gifts Direct or Organic Foods Direct services. Other supplies, such as wine and groceries, will be decided on a branch by branch basis.
Unlike its retail stores, whose deliveries rely on a central reserve of fuel, Web order carriers are dependent on local petrol supplies.
Other Internet food retailers are also being hit by the ongoing fuel shortages. Tesco has formed a crisis group in an attempt to keep its online delivery service running.