Brunswick beat rivals Finsbury and Financial Dynamics to secure its five-year relationship with the airline after a pitch, which initially involved seven City agencies.
The final stages of the review saw Brunswick founder Parker and Finsbury co-founder Roland Rudd pitch head-to-head.
BA head of corporate communications Iain Burns said the agency will no longer provide day-to-day PR support, instead fulfilling a high-end strategic counsel role in support of the in-house PR team.
'The selection process was a very close call and Brunswick was pushed all the way by some great agencies,' said Burns.
'As the in-house corporate team has grown in expertise we've been able to find a different way of working with Brunswick to reflect the lower levels of consultancy support.'
It is understood Brunswick founder Alan Parker will act as senior adviser on the account, which runs for two years.
Parker will report directly into Burns.
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