Eastern Electricity, the largest regional supplier, wants Offer to focus on smaller companies which typically have higher bills. It is thought that this view is supported by other large companies, including Southern Electric.
Eastern argues that a "typical" bill varies by as much as 15 per cent across the country, with some of the smaller firms having the highest bills. It says that any review should aim to even this out. The company has put its ideas to Professor Stephen Littlechild, the director general of Offer.
Some firms are also angry at Northern Electric, which proposed a package of £500m in shareholder sweeteners and thus helping to bring down the wrath of Professor Littlechild on the sector.
The sweeteners, part of Northern's defence against a hostile takeover bid by Trafalgar House, would have increased Northern's gearing to more than 200 per cent. That proposal, along with increases in electricity share prices, prompted Professor Littlechild to overturn price controls agreed in August. A further clampdown on electricity distribution prices across the sector is expected as a result.
John Devaney, chief executive of Eastern, said: "We are pretty annoyed at Northern's defence and the way it has misled the regulator into believing that there is a need for a wide review. Now we are saying that the problem was Northern's not the industry's.
"Professor Littlechild should look at small companies which are bid targets," he added.
Mr Devaney also said that small companies have been allowed the same overhead allowance as larger companies when Offer set the previous price controls and he argues that this should be changed in the current review.
Industry observers say that the companies most vulnerable to bids are Northern, Manweb, South Western Electricity and South Wales Electricity. These are amongst the smallest in the sector.