The strikes stem from BA's decision last November to cut cabin crew pay and alter staffing levels on its flights.
BA Chief Executive Willie Walsh and leaders of labor union Unite, which represents cabin staff, blame each other for a breakdown in communication.
BA is trying to reach a deal with Unite which will save 62.5 million pounds a year to counter falling demand, volatile fuel prices and greater competition.
Unite said on Friday no talks to avert the strike were planned, while BA said the conciliation service ACAS was trying to arrange discussions between the two parties.
Talks over the past six months have failed to yield a resolution, with the walkouts having caused BA to ground flights on 17 occasions so far.
The issue of travel allowances for cabin crew has become a serious sticking point in the conflict, which comes at a difficult time for BA. Last month, the airline announced a full-year loss of 531 million pounds.
The latest strike took place less than a week before the start of the soccer World Cup in South Africa and followed a five-day stoppage which ended on Thursday. There was a four-day walkout last week and seven days of stoppages in March.
With the World Cup in mind, BA said this week it would fly a full schedule to South Africa.
BA plans to operate 80 percent of long-haul flights from London's Heathrow and 60 percent of short-haul services from the airport during the latest strike. Flights from the capital's Gatwick and City airports are unaffected.
BA, Europe's third-largest airline, said the total cost of the stoppages could be assessed only at the end of the disruption and would reflect lost bookings offset by some volume driven cost savings.
Analysts believe the strikes could put off previously loyal BA customers from flying with it in future and hit its hopes of breaking-even in 2010-11.
BA carried 11.5 percent fewer passenger in May year-on-year because of the strikes, leaving it lagging rivals such as Air France-KLM, Ryanair and easyJet whose passenger numbers are rising.
BA shares, which have risen 10 percent this year, closed at 201 pence on Friday, valuing the airline at about 2.3 billion pounds.
