The energy giant made the payments to domestic and micro-business customers after its third-party agents missed appointments or turned up late, and did not compensate them as required by the regulator Ofgem.
Around 12,000 mostly business customers were affected.
British Gas reported the breach to Ofgem, which agreed to its redress package and is therefore not taking formal enforcement action.
Martin Crouch, Ofgem senior partner for improving regulation, said: "British Gas did the right thing in coming forward to report this issue, and has since improved its processes to make sure that, when appointments are missed or not kept on time, all customers receive the compensation they're entitled to.
"It's crucial that suppliers keep appointments on time, and make amends when things go wrong."
As part of the compensation package, British Gas paid out £30 for an initial failed appointment and £30 for not paying customers within the required 10 days.
In addition, the group has paid an extra £30 to each affected customer.
Energy suppliers and their agents must meet minimum standards of customer service under Ofgem's Guaranteed Standards, including when they visit premises. When they fall short, customers must be paid compensation.
A British Gas spokesman said: "We discovered the error last year and reported it to Ofgem. We have apologised to the affected customers, given them all compensation and an additional goodwill payment.
"In April this year we introduced new system checks to ensure this can't happen again."