Over last weekend's initial three-day strike, BA posted a series of YouTube videos addressing customer concerns and issued a press ad in the form of a letter from its chief executive, Willie Walsh.
The survey of 1000 consumers, carried out with market research company Toluna, found that the majority of those who had seen BA's campaign have either retained or improved their perception of the brand.
Nearly 19% had an enhanced view of the airline, while the sentiments of 64% were unchanged. Only 17% said they had a diminished opinion of it.
The push has also shored up public support for BA in its dispute with trade union Unite.
More than three-quarters of those who had encountered BA's communications felt as supportive of the airline or more so than before and 24% said their support had lessened.
A further four-day walkout is planned for 27 March, but Unite has appealed to BA chairman Martin Broughton, to instigate fresh negotiations.
Chris Davies, head of digital marketing, said social media is certain to take an increasing role in BA's marketing, following the strike activity.
He said: "Although we will continue to use traditional channels, putting social media at the heart of our overall communication has allowed us to take a fleet of foot approach."