Heathrow airport has asked airlines to halve the number of passengers they fly into the airport next week to try to minimise disruption caused by a strike.
Its operator BAA warned of "gridlock" and said passengers could face 12-hour delays on Wednesday when immigration officers go on strike over pensions.
BAA said it was holding talks with airlines and the UK Border Agency.
PM David Cameron said it was clear there would be an impact at ports and airports, but borders would be secure.
"At the very least there will be longer queues and people will have to wait longer at borders," his spokesman said.
He added the government was still working on contingency plans and gathering information on the impact of the strikes.
'Held on aircraft'
Virgin Atlantic said it was "very concerned", adding it would allow passengers booked on inbound flights on Wednesday to rebook for travel up to four days earlier or later.
BA said it was doing everything it could to protect its customers and they could switch flights free of charge.
BMI said it planned to operate as normal and was also working to minimise disruption, while Cathay Pacific urged its passengers to postpone and rebook their flights.
In a letter to all airlines operating into Heathrow, chief operating officer Norman Boivin said: "The delays at immigration are likely to be so long that passengers could not be safely accommodated within the terminals and would need to be held on arriving aircraft.
"This in turn would quickly create gridlock at the airport with no available aircraft parking stands, mass cancellations or departing aircraft and diversions outside the UK for arriving aircraft."
BBC transport correspondent Richard Lister said aviation officials were working on the basis that immigration staffing levels would be at a maximum of 30-50%, and that most of those checking passports would have no experience and little training.
During the summer strike, border agency managers ran passport control but this time they are expected to strike too, our correspondent added.
Lucy Morton, deputy general secretary of the Immigration Services Union, said she regretted its members were striking.
"This union hasn't taken industrial action at all in its 28-year history. This is something our members feel deeply and desperately strongly about, but nonetheless it's no-one's wish to disrupt the border, or to cause chaos to the travelling public. It's the only way we have left to get the government to hear us."
She added that although she believed they would not have public sympathy for the action, she wanted it to be effective so they would not have to take further action.
The warning from Heathrow, which handles more international passengers than any other airport, came after immigration staff voted to join the strike by public sector workers.
Strikes are being held over changes to public sector pensions and thousands of border agency workers are expected to be among up to two million who could walk out.
Scott Stanley, Gatwick airport's chief operating officer, said the strikes were likely to affect arriving flights at airports across the UK and warned passengers to be prepared.
"Unfortunately, airport staff cannot man the desks at the border zone but we will provide all necessary assistance to the Border Agency," he added.
He said hundreds of airport volunteers planned to come in to help and all non-essential work and meetings had been cancelled.
- Stansted airport said the strike would have less of an impact than at Heathrow, and airlines were not being advised to reduce passenger numbers
- Southampton airport said disruption would be "minimal" on international flights, with no impact domestically
- Newcastle International airport said it would operate as normal, with the only "potential impact" on longer processing times for inbound passengers
- Manchester airport said passengers should expect longer than normal waits during busy periods, but no "significant disruption"
- Edinburgh airport said it was expecting minimal disruption and that it was still consulting with UK Border Agency to work out contingency plans
- Glasgow airport said it was establishing what impact the strike would have
- Aberdeen airport said it did not expect to be affected
On Wednesday it emerged that civil servants were being asked to act as airport border staff during the strike action.
The Home Office is pulling in border agency staff who are not union members and civil servants from Whitehall to carry out immigration checks.
In a statement, the department said it was too early to speculate on how many people would join the strike, and that it was exploring all options to minimise disruption.
Rob Whiteman, chief executive of the UK Border Agency, said they had spent the last weeks and months considering all options to ensure they were prepared for union action.
Disruption at the UK's largest airport is expected to be particularly severe because nearly 100 long-haul services are due to arrive before 09:00 GMT on the day of the strike.
Meanwhile, former Labour Home Secretary Alan Johnson indicated he was backing next week's strike - a stance that is at odds with his party.
Unions say proposals which require their members to work longer before collecting their pension and contribute more are unfair, but the government says change is needed to keep down the cost to the taxpayer, because people are living longer.
Simon Walker, director general of the Institute of Directors, said the strike would be a disaster for the UK and questioned whether it should be allowed.
Meanwhile, it has been confirmed that no buses or trains will operate across Northern Ireland next Wednesday due to the strike.