The move comes in a bid to protect passenger journeys in response to a request from Border Force to Heathrow that passengers numbers are in line with the capacity it can serve.
Around 1,000 passport control workers are set to walk out on 23-26 and 28-31 December at Birmingham, Cardiff, Glasgow, Gatwick, Heathrow and Manchester airports.
Both Virgin Atlantic and British Airways have stopped the sale of tickets for arriving flights on the strike dates only.
The airlines are offering customers who are due to fly on a strike day the option to change their flight to a day when there is no industrial action.
A BA spokesperson said: "In view of the Border Force strikes planned over the Christmas period, we’re continuing to work closely with the UK government, Border Force and airport authorities to ensure that we play our part in ensuring our customers are able to travel as planned at this important time of year.
"We’re offering anyone booked to travel on an international flight into Heathrow or Gatwick airport on strike dates the option to change their flight dates."
A Virgin Atlantic spokesperson said: "We continue to work closely with UK government and airport partners at Heathrow and Manchester to support contingency planning and minimise the impact of Border Force strikes on our customers’ journeys.
"Our priority is getting our customers to where they need to be this festive season, ensuring they’re aware of the strikes in advance and prepared for longer waits at border control.
"We intend to operate our schedule as planned, with additional flexibility to allow customers to change their flight dates if they wish to avoid arriving on strike days."
