The airline has been in negotiation with the British Airline Pilots Association (Balpa), which is thought to represent about 60% of its pilots, over allowances and expenses paid to pilots as part of their job.
The move has angered representatives of the Professional Pilots Union (PPU), who claim to represent as many as 280 of the airline’s 900 pilots but have been left out of the talks.
Now, the PPU is conducting a ballot of members, which could see a strike in a month’s time at the earliest, although a spokesperson added they have been heartened by an apparent change of heart by Virgin.
He added: “Despite the PPU representing a significant number of Virgin Atlantic pilots, the airline refuses to recognise it in any negotiations over its members’ pay and conditions.
“Our issue is not about money, simply the right to be represented by a chosen union. It represents zero cost to the company.
“Within 24 hours of informing the company of our intention to ballot our members on industrial action, we have suddenly been offered last-ditch talks on Friday to avert strike action.
“We are encouraged by this offer and hope that genuine progress can be made.”
A Virgin spokesperson said: “Currently, we have no active industrial dispute with our pilots.
“We’re aware of reports that the PPU, which represents a minority of our pilot workforce, may be considering a ballot for industrial action over union recognition.
“We value our pilot workforce enormously and have an ongoing and constructive relationship with our recognised union, Balpa.
“We’ve also been encouraged by the discussions that started earlier this year between Balpa and the PPU, in an attempt to identify a framework for working together.
“We would like to reassure customers that all Virgin Atlantic flights continue to operate as normal.”
A Balpa spokesperson added: "Balpa is the majority pilot union in Virgin Atlantic, and we continue to represent all Virgin Atlantic pilots for collective bargaining through our long-established recognition agreement.
"We have been engaged in constructive discussions with the PPU in recent months, so this step is somewhat surprising.”