Many of the customer grievances relate to estimated readings, which instead of calculating the bill from meter readings, predicts the amount of gas the household has used.
However 15,456 customers called the company to register their complaint over the new style of bill which many claimed overcharged them.
Another common problem for customers was out-of-date or incorrect account and contact details.
British Gas say they have employed 800 new staff to deal with complaints amid reports of problems with the company's new database system which will hold account details for 16 million customers.
"Our new managing director Phil Bentley, who started work in March, has made a personal commitment to putting our customer service level back to where it should be as one of the UK's top rated energy suppliers and we're already seeing clear signs of improvement, having recruited an additional 800 staff to help call answering," a spokesperson for British Gas said.
However Energywatch said many customers found British Gas' customer service "unforgivable".
"Their inability to deal with customers’ problems is inexcusable – customers should not be left hanging on the phone or having to explain their circumstances to several different advisers," said Adam Scorer, director of campaigns at the watchdog.
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