Airline warn that a strike by Border Agency staff could cause delays of up to 12 hours.
However, most airlines insist they will continue to operate normal services throughout the day despite fears that airports could grind to a standstill.
British Airways said that it is still planning to operate "a normal schedule" in the face of a plea from airports operator BAA that airlines halve the number of passengers landing on Wednesday.
Virgin Atlantic said over 1,000 passengers - one third of its total capacity - had changed their flights to avoid landing in the UK on Wednesday and BA said many of its passengers had also altered their travel plans although it refused to give numbers.
Heathrow Airport said this morning it was waiting to hear from airlines how much they had managed to reduce their loads following warnings from airport operator BAA that it could take 12 hours for passengers to get through immigration when staff join a strike by public sector workers.
A spokesman for the Home Office this morning denied reports that the police would be drafted in to replace Border Agency staff. He said it was considering "all options" to secure the UK's borders, but he said no decision had been taken.
"At the moment, this is just speculation. We are looking at all options, including using the police and the military. We have also asked staff to volunteer from other government departments if they are needed.
"A decision will be taken when we know the extent of the strike action."
EasyJet acknowledged that disruption to immigration services could start at early as 1800hrs on Tuesday but it said it too planned to continue with a normal service. A message on its website said: "If this changes due to unfolding circumstances this website will be updated. As such, we would advise all passengers to check the status of their flight before heading to the airport on these dates."
A spokeswoman for Gatwick Airport said: "A lot of airlines are continuing to stick to their normal schedules on Wednesday, but it is not the job of the airport to tell them what flights to operate."
She said the airport would attempt to ensure there were adequate facilities for arriving passengers held in queues, such as food, water and toilets.
Abu Dhabi-based Etihad Airways has cancelled two flights to Heathrow and one departing flight on Wednesday and reduced capacity on a third flight from Abu Dhabi to the London airport, but it says all flights to Manchester will operate as planned.
Source: Travelmole
