They said the inquiry, which was launched at the end of July, has been muddled, slow, and is using a new economic model that appears unworkable.
One of the major supermarkets said: "The OFT is trying to get to grips with a new method of calculating profitability. But even they do not seem to fully understand it."
The OFT launched the inquiry to establish whether the major supermarkets are making excessive profits.
The key charge levelled against the supermarket majors - Tesco, Sainsbury, Asda and Safeway - is that they are profiteering by using their market power to drive down the costs paid to suppliers, but failing to pass on those benefits to consumers in the form of lower prices.
However, the top supermarkets say that although the OFT is demanding huge quantities of information, they are asking no questions about supplier relationships.
The supermarkets were surprised by the omission as it was a report by the Welsh Affairs Committee into the crisis in Welsh farming that triggered the OFT's investigation.
That report concluded that prices charged on the supermarkets' shelves for beef and lamb bore no relation to the prices paid to farmers.
"They are asking for mountains of data, as you would expect. But most of it is accounting information; there is nothing on supplier relationships," said one supermarket.
The other key concern is the new economic model being used by the OFT to determine excess profitability. The model was devised by Martin Graham, chief financial analyst at the OFT, and Anthony Steele of the University of Warwick. It was published last year in an OFT research paper.
Critics say that though the model looks fine in theory, it is impossible to see how it will work in practice. One supermarket director described it as "severely econometric"- meaning it was overly statistical.
The willingness of the supermarkets to criticise the OFT is surprising as they risk a backlash from regulatory authorities.
But, in this case, the OFT itself has taken the unusual step of commenting on an investigation in progress. One of its officials has said that the inquiry will determine whether the competition between the supermarkets is "red in tooth and claw".
One supermarket said the OFT might be "playing to the gallery" following a number of reports suggesting that British consumers pay far higher prices for their groceries than people in France and Germany.
The OFT has yet to issue the supermarkets with its formal questionnaire but has said it will report its findings by December. It last investigated the supermarkets in the early 1980s but found no case to answer.
In July John Bridgeman, director general of fair trading, said that although he had no specific evidence to reverse his previously held conclusion that consumers are not being disadvantaged, the time was right for a detailed study.Reuse content