The first walkout by the airline's cabin crew for 13 years sparked a war of words between the two sides, while the political heat on Prime Minister Gordon Brown was also stepped up.
The Conservatives released a new advert depicting the Prime Minister as a pilot, wearing a Unite cap, and bearing the message: "Gordon's Doing Sweet BA".
BA claimed that around 50% of cabin crew staff had turned up for work at Heathrow, but the union insisted that 80% of its 12,000 members had supported the first day of a three-day walkout.
The union said BA's Terminal 5 at Heathrow was like a "ghost town", adding that the airline contingency plans were failing.
BA described the union's claims as "rubbish", and said it had reinstated some long-haul flights this weekend because more staff had worked, including services to Miami, Los Angeles, Tel Aviv, JFK in New York and Cape Town.
Union officials claimed that, during a two-hour period in the middle of the day, just 10 flights left Heathrow instead of the normal 50.
BA said the day got off to a "good start" with its contingency plans, adding later that, because 50% of cabin crew had turned up at Heathrow, it was moving to reinstate some short and long-haul flights.
A BA spokeswoman said: "Cabin crew are continuing to report as normal at Gatwick and the numbers reporting at Heathrow are above the levels we needed to operate our published schedule.
"At Heathrow, around 50% of cabin crew have reported as normal and we are therefore increasing the number of long-haul and short-haul flights in our schedule in the days ahead."
The company said it was confident of handling as many as 49,000 passengers today and the same number tomorrow, which compares with a figure of around 75,000 for a normal weekend day in March.
Some passengers are due to travel with other carriers on specially chartered planes.
BA has arranged with more than 60 other airlines to take BA customers on their flights.
Some passengers brought forward flights booked for this weekend and Monday but were left disappointed when they arrived at Heathrow yesterday to find earlier flights had been overbooked and they were not guaranteed a seat.
Unite claimed a number of planes were stacked up at airports as a result of the strike, including 85 parked planes at Heathrow, 20 at Cardiff and 20 in Shannon.
Picket lines were mounted at airports including Heathrow, and Unite said that no buses which normally transport crew to work had crossed them.
A Unite spokesman said: "The support we are getting shows how strongly people feel about this and is in spite of the bullying by management.
"Willie Walsh's appeal for people to cross our picket lines has obviously not worked."
Unite's joint leader, Tony Woodley, accused BA of wanting a "war" with the union and complained that BA chief executive Willie Walsh had tabled a worse offer than one withdrawn last week.
Mr Woodley said he had been set "mission impossible" because of the new offer, which included a four-year pay deal the union maintained would at best freeze wages until 2014.
The union had offered a 2.6% pay cut this year as part of a three-year deal.
Unite also claimed today that BA had failed to commit to extending the validity of the current industrial action ballot so members could vote on any offer from BA.
"This failure could have led, in the event of a rejection of BA's proposals by cabin crew, to a third strike ballot in five months - and continued instability for the airline, its customers and the wider BA workforce," said a Unite official.
Mr Woodley said: "The disruption that passengers will inevitably experience over the next three days could have been spared had BA grasped that you cannot put an offer on the table one day, take it off the next and then come back with a worse one a few days later."
The atmosphere in Heathrow's Terminal 5 was described as relaxed by observers.
The only difference to most travellers' flights was that many were operated by other companies as BA sought to make sure its passengers got to their destinations.
Long-haul flights in particular seemed not to be disrupted.
American Jodi Rogers, 39, was flying to Boston after a 10-day holiday.
"As far as I know we are flying with BA and it's on time," she said.
"It was shortly after we landed here that we heard there was going to be a strike, which did concern us as we thought we may not be able to get home, but so far there has been no trouble."
But Par Svensson, 47, from Sweden, had his flight to Copenhagen cancelled this morning due to the strike and he was waiting at the terminal to see whether he could get a later flight from Heathrow.
Unite assistant general secretary Len McCluskey told hundreds of strikers at a rally near Heathrow that "intransigent management" could be defeated.
He said: "Our challenge to Willie Walsh is that he needs to let his cabin crew speak publicly about the real cause of this dispute.
"Decent men and women are terrified about speaking out about this fight for their futures for fear of reprisals.
"Isn't Willie Walsh ashamed that his employees are having to speak with their backs to TV cameras and their voices distorted? That stewardesses are covering their faces going into meetings to avoid identification?
"This is not just bad industrial relations - it's an offence against democracy. Willie Walsh should remember this is Britain, not Burma."
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