Downing Street is urging British Airways and the union representing its pilots to “sort out” their dispute and avert planned strike action.
Walkouts by members of the British Airline Pilots Association (Balpa) are due to take place next Monday and Tuesday in a row over pay.
BA has warned passengers with a flight booked on or around those dates that they face disruption and are unlikely to be able to travel as planned.
A No 10 spokeswoman said: “Nobody should have their travel plans disrupted or their holidays ruined.
“The unions and BA need to get round the table and sort this out. The public would expect nothing less.”
Balpa general secretary Brian Strutton said: “We have offered to get back round the table and have been refused.
“The gap between what we’re asking for and BA is just £5m – much less than the £40m it will cost per day of strike action.
“Rooms are available at [the conciliation service] Acas today and Balpa is willing to talk – where is BA?
“Since they’ve offered, perhaps Downing Street or the secretary of state for transport could assist in calling both sides for talks – Balpa would be there.”
BA has said it was open to “constructive talks on the basis that there are no preconditions”.
A spokesman said: “Balpa has cynically waited until we have helped the vast majority of customers with alternative travel arrangements, and our planning for a strike has reached a critical stage.
“Our customers need the certainty that Balpa will call off the strikes for good, not just for two days next week.”
BA said it has emailed customers travelling on affected flights next week, but urged people to check their flight status.
Another strike is planned for 27 September.
The airline added that it will contact customers in the next few weeks if their flight is affected.