Cabin crew began a second five-day strike on Sunday, coinciding with a week of school holidays in Britain, after talks between Unite and the airline failed to reach agreement last week.
Another five-day strike, stemming from a long-running dispute over the airline's cost-cutting drive and staffing levels, is due to start on June 5, less than a week before the start of the soccer World Cup in South Africa.
Unite said the stoppages had cost BA at total of 105 million pounds so far. BA said it did not recognize the figure and it was too early to put a price on the overall disruption.
However, BA has said seven days of walkouts in March cost it 43 million pounds ($63 million).
Mediation service Acas is overseeing the talks at an undisclosed location after left-wing protesters disrupted a previous round of talks.
BA said it had been operating 70 percent of long-haul flights from London Heathrow and 55 percent of short-haul services from the airport during the latest strike. Flights out of London Gatwick and City airports were unaffected.
The airline said it planned to increase to more than 80 percent of long-haul flights from Heathrow if next week's strike goes ahead and 60 percent of short-haul flights.
With the World Cup in mind, BA said it would fly a full schedule to South Africa.
Unite has said it could hold a further ballot for strike action during the peak summer holiday months of July and August.
Last month, BA reported a second straight year of record losses and is battling a global economic downturn and industry-wide recession as well as disruption caused by volcanic ash drifting over Europe from Iceland.
Both sides in the dispute have claimed that a deal over pay and cuts to staffing levels and travel was not too far away but have blamed each other for the lack of progress.
(Editing by Will Waterman, Michael Shields and Karen Foster)