Some media reports said as many as 100,000 passengers were affected by the strike led by check-in staff.
BA management accused unions of walking away after day-long talks which failed to end a row over plans to introduce a new, electronic clock-in system.
Despite the dispute, BA said it would go ahead with the switch from the current paper-based method of signing in to the new swipe-card technology, from midday (1100 GMT) on Wednesday.
Staff say the new system could force them to go home during quiet periods and force them to return on busier days. BA dismissed the claims.
BA has come under fire for introducing the new technology during the peak summer period.
The break-down in talks came after British Airways cleared about 700 stranded and frustrated passengers at Heathrow.
Over the weekend the airline was forced to cancel more than 360 flights at three of Heathrow’s four terminals, causing chaos that left 80,000 travellers stranded.
Check-in staff went on strike on Friday evening and throughout Saturday.
The saga has been a public relations disaster for BA, which prides itself on offering smoother, more punctual services than its rivals, particularly low-cost carriers that have been muscling in on its business.