The council said its staff had "never experienced such anger and frustration" in consumers' complaints.
Complaints have nearly doubled over the past year and last month reached "by far" the highest total since the company was privatised in 1986.
The council blames the loss of 25,000 jobs, the reduction of £600m in annual group operating costs and the abandonment of services which the company "sees no money in", such as the service and repair of cookers.
Much of this programme has been initiated by British Gas to ready itself for the opening of the gas market to competition from next year. The company has reorganised its UK operation into five separate business units and reduced showroom services and spending on safety checks.
The council says the volume of complaints reinforces its view that there is "tension between the aims of the Citizen's Charter and the principles of free-market economics".
The charter aimed to raise standards of public services "up to and beyond the best at present available and to make them answer better to the needs of ordinary people".
In 1993, British Gas won a CharterMark for "excellence in delivering public service" after two years in which complaints had fallen. But last year complaints rose by 19 per cent compared with 1993 and continued to increase throughout the year.
Last month there were 5,246 complaints, compared with 1,925 in January 1994, a rise of 172 per cent. The previous record was 3,670 in November 1988. There was also a price rise last month although services were "evidently worse".
Ian Powe, director of the council, said that it was unclear whether British Gas had been "temporarily blown off course by the winds of change now rushing through the gas industry" or had deliberately changed course to spend less on customer care.
"The answer probably lies somewhere in the middle but, either way, the pace of change has outstripped public patience. If British Gas wants to keep market share after 1996 it must recapture consumer confidence."
All the complaints were "substantial". Customers were finding it much harder to get through to British Gas by telephone and when put through, found the person contacted "did not know the answer".
"Complaints are beginning to indicate discourtesy by British Gas showroom staff, to customers who want service or information that has been withdrawn and by staff in general who tell people to `go elsewhere' if not satisfied by what British Gas now offers. Untrained agency staff, brought in to fill gaps left by too-rapid a redundancy programme, are not giving the helpful service offered by those whose jobs have gone."
The company's preparation for a competitive gas market has been accompanied by growing criticism, not least of the 75 per cent pay increase given to its chief executive Cedric Brown. Nigel Griffiths, Labour's consumer spokesman, said the figures "justify all the concerns Labour has raised in recent months".
Norman Blacker, executive director of British Gas, described the figures as a "temporary reversal of a downward trend in customer complaints" caused by the "biggest reorganisation ever undertaken by any British utility company". He added: "We shall end up with a far slimmer, less bureaucratic company, better able to focus on the needs of our customers and the expectations of shareholders."