Alex Cruz, chairman and chief executive of British Airways, said in a statement the company is "surprised and disappointed" by the fine.
"British Airways responded quickly to a criminal act to steal customers' data," he said. "We have found no evidence of fraud/fraudulent activity on accounts linked to the theft. We apologise to our customers for any inconvenience this event caused."
The Information Commissioner's Office said British Airways has cooperated with the investigation. Still, the office proposed the record penalty of 183.39 million pounds ( NZ $344.72 million), or about 1.5 percent of British Airways' annual revenue, under the General Data Protection Regulation which was passed by the European Union last year.
British Airways, which is owned by International Airlines Group, said it has since improved its security. IAG's chief executive Willie Walsh said in a statement that the airline would fight the proposed penalty.
"We intend to take all appropriate steps to defend the airline's position vigorously, including making any necessary appeals," Walsh said.
IAG's stock dropped by nearly 1.4 percent by late afternoon on the London Exchange.