Sir Richard Branson has written a letter to Virgin Atlantic pilots asking them to reconsider striking.
British Airline Pilot's Association (BALPA) is threatening industrial action in protest of its members having not received pay rises since 2008 and the 2011-2013 pay offers being insufficient to keep up with inflation.
In his letter, Branson writes that unless the British Airline Pilot's Association (BALPA) promises to withdraw its threat to take action "very soon", it will leave an "indelible scar on the company" and "impact customers' trust".
The strike could come at the "worst time for families", said Bob Atkinson, spokesperson for travelsupermarket.com.
"With the strikes potentially taking part in the busiest part of the year, huge numbers of families will have their holidays ruined," he added.
Branson, who admits not taking an active role managing the airline for a number of years, says he has looked at all the facts and thinks the airline has made "the best offer it can". He said: "The balancing act our chief operating officer and board have is that if we go further for one sector of the workforce, especially in these difficult times for everybody, we have to do the same for all sectors.
"And from looking at the figures it will mean asking the public to pay higher fares and in this difficult economic climate, we simply cannot do that at this time."
BALPA is expected to announce dates of its strike action tomorrow. Jim McAuslan, general secretary for BALPA, says Virgin's pilots don't want to strike but they have "absolute resolve to secure a fair settlement".
If my holiday plans are affected, what can I do?
Atkinson advises holidaymakers who have flights booked with Virgin to ensure they have appropriate travel insurance as soon as possible: "It is vital that all passengers have travel insurance that has a strike clause within it. You can still take out cover up until the union announces specific dates of action.
"This will then cover you against any potential losses should your flight or holiday and travel plans be disrupted."
He also suggests contacting the airline, tour operator or travel agent you booked with to ensure it has the most up-to-date contact information to be informed of strike action.
Am I covered?
Holidaymakers who have booked a package deal through Virgin Holidays are protected under the holiday financial protection scheme ATOL and will be entitled to either a full refund or alternative flights or alternative flight dates.
Those who have booked flights direct with Virgin receive the same level of protection under EU261 regulations; however, Atkinson warns while passengers should be able to get their money back, or make alternative travel plans, many will still have their summer holidays disrupted:
"The problem is that on popular summer routes to places such as Florida and Dubai, these flights are already going to be choc a bloc – so Virgin will have nowhere to put its passengers."