The OFT - the government's consumer watchdog - confirmed that it is examining the supermarkets' pricing online, and that it has already held talks with the companies concerned, but refused to comment further on the nature or outcome of the discussions.
What it is thought to be investigating are claims that companies such as Tesco, Sainsbury's and Asda are charging higher prices for products bought online than in their stores - a reference to the 'guide' prices offered by online grocers to account for the fact that some local stores offer the same product at different prices depending on promotions. This can mean that some shoppers are in fact charged more than the price listed on the site, critics claim.
Other accusations include charging for premium products but sending standard ones and using online grocery operations to push through products such as fruit and vegetables which are near their sell-by date. The practice of selecting 'alternative' products for goods which are ordered but out-of-stock is also being called into question.
As the UK's biggest online retailer with profits of £28 million last year, Tesco.com is bearing the brunt of the investigation - although it, like Asda and Sainsbury, has denied that it charges higher prices for its online groceries.
Tesco's online offer extends well beyond food - books, clothes, DVDs, music and even banking services are available through the company's website, which is accessed by many UK shoppers using Tesco.net, the company's own Internet Service Provider (ISP).
The company has been by far the most successful online grocer in the UK, offering the service across the country using its stores as depots for deliveries. Rival Sainsbury's launched its service using dedicated warehouses, a far less cost-effective means of fulfilling orders.
But both companies have invested in new technology recently in a bid to improve the quality of the service they offer.
Tesco recently supplied 300 of its largest stores with the technology to build the latest generation of 'Smart' shopping trolleys - display panels which, when attached to shopping trolleys, show customer shopping lists and allow Tesco's staff to pick goods more effectively by guiding them through the store to the correct aisle and shelf.
Sainsbury's, meanwhile, has fitted 400 of its delivery vehicles with new satellite navigation equipment which it claims will allow it to avoid the ubiquitous British traffic jams and ensure timely deliveries. This, it claims, also allows it to fit in more deliveries each day, making the service more cost-effective.
The investment by the leading players in their online businesses - part of the wider move towards offering a full range of added-value services to offset the perennial low margins of most food retailing - clearly shows the importance of the Internet to the big UK supermarkets.
Any revelations by the OFT of malpractice are likely to seriously hamper growth in Internet sales, a market where trust (in the safety of the service but also the integrity of the service provider) is such an important commodity.