Tony Woodley, joint leader of trade union Unite, said a new ballot for strikes could be only a week or so away, as union members continued with the current five-day walkout.
A fresh ballot will be needed because the 12-week protective legal period for taking industrial action ends in early June.
Union leaders have warned British Airways that it could face a 'needless summer of disruption' because of the stance of its chief executive over the ongoing cabin crew dispute.
Mr Woodley said if crew were forced to seek a new mandate for industrial action the blame for this will lie 'firmly' with Mr Walsh and his 'persistent refusal' to permit a peaceful settlement.
The union leader has accused the airline of intimidating staff and victimising trade union members.
In his speech this afternoon, Mr Woodley said 'there is only one thing to do with bullies - that is stand up to them until they learn some manners.'
Unite is planning another five-day strike next week unless the deadlock is broken. Any further strikes are likely to be in July as it will take Unite four to five weeks to organise a new ballot.
According to the union, the dispute has cost BA £91m (€107m) so far, with each day of action costing £7m (€8.2m).
BA said it had operated more services than planned yesterday, including the reintroduction of all of its services from Heathrow to New York's JFK airport, adding that it would continue to add to its schedule where possible.
On 17 May, British Airways won a dramatic eleventh hour injunction that halted strike action planned by thousands of its cabin crew in a bitter row over jobs, pay and staffing levels.
BA chief executive Willie Walsh then responded that he hoped the injunction gave the union a chance to pause and consider again the 'very fair' offer BA had made.
