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.
