It is yet to be decided whether a new senior external comms leader will be recruited following the elimination of Marston's role.
Head of internal comms Amanda Poole is also leaving, as the airline places employee comms under its people and legal department, further reducing the remit of the comms team.
The decision was made by chief executive Alex Cruz and communicated to staff last week.
BA is hiring Drew McMillan, head of colleague communication and engagement at Virgin Trains, to lead its internal comms function. He will report to Maria De Cunha, who is the carrier’s director of people and legal. McMillan, who has twenty years' of internal comms experience, joins early next month.
The decision leaves head of global PR Kathryn Williamson and head of global news Sophie Greenyer as British Airways' most senior comms staff. Both will report into the CEO.
Marston, who joined BA in 2005 from his job as transport correspondent on the Daily Telegraph, said: "I’ve had a great 12 years at British Airways, and I’m looking forward to whatever new opportunities may come along."
Poole has been with the airline just as long, serving as Marston’s deputy when he first joined BA.
BA said the comms restructure would not affect the pitch process for its PR agencies contracts, which began last year.
Strengthen staff engagement
In a statement to PRWeek, BA said: "The greatest asset of British Airways is our people. We want to strengthen our engagement with our 45,000 people by consolidating our excellent internal communications team within our HR department."
"Paul has played a big part in the success of British Airways over many years. He has chosen this moment to take his leave and we wish him every success in his future career.
"Amanda has led our internal communications with great distinction for six years. She has decided now to pursue new opportunities and we wish her every success in the future."
Despite some successful route launches, digital communications innovation and a tie-in with Great Britain's Olympic team over the past couple of years, British Airways suffered a major reputational crisis last May following a catastrophic IT failure, which left thousands of travellers stranded.
The airline has also been criticised for the problematic introduction of paid-for food by Marks & Spencer and cutbacks in legroom for economy passengers.
McMillan was the Virgin Trains employee who announced its shortlived decision to stop stocking the Daily Mail on board its services, in a statement circulated to staff in November, before being brought to public attention by PRWeek earlier this month.