Electricity consumer groups have called for about £1bn to be cut from electricity bills over the next four to five years in addition to cuts of £2.5bn announced by the watchdog, Offer, last August.
The chairmen of regional Electricity Consumer Committees - appointed by Offer but acting independently - also said that a further £1bn should be given in customer rebates if the £4bn sale of the National Grid Company goes ahead.
The ECC demands come in the midst of a review of electricity distribution prices by Professor Stephen Littlechild, director-general of Offer, less than a year after the £2.5bn package of controls was agreed with the 12 regional companies in England and Wales.
Professor Littlechild shocked the sector in March by announcing he would revisit the controls after seeing large and sustained increases in the share price of the regional electricity companies and other evidence of financial strength.
Yvonne Constance, who heads a committee of the ECC chairmen, said that in retrospect Professor Littlechild "was neither tough enough nor were we sceptical enough" when the previous price controls were set.
She admitted the ECC gave a "qualified welcome" to the earlier review but said that more was understood about the companies, including how much they were prepared to borrow.
She said: "Since privatisation share prices have risen dramatically and dividends have grown each year. Profit levels in the electricity industry demonstrate that there is scope to redress the balance and to ensure that ordinary customers receive a better deal."
The ECC chairmen are asking Professor Littlechild to impose a 10 per cent cut in distribution prices in 1996 following one-off cuts of up to 17 per cent that he forced on the companies last month. They then want him to replace the cap agreed last August of inflation minus two percentage points with "RPI minus five". Distribution accounts for only about a quarter of the final bill.