Heathrow airport has been ordered by the Border Force to stop handing out leaflets to passengers acknowledging the "very long delays" at immigration.
Amid increasing anger at the length of queues for travellers arriving at border control, airport operator BAA has tried to defuse tensions with a leaflet apologising for the problems.
It said people arriving in the country "deserved a warmer welcome" and explained how to complain to the Home Office.
But Marc Owen, director of UK Border Agency operations at Heathrow, has told BAA that the leaflets are "inappropriate" and that ministers would take "a very dim view".
In an email obtained by The Daily Telegraph, he said: "The leaflet... is both inflammatory and likely to increase tensions in arrivals halls especially in the current atmosphere.
"It is inappropriate in that it is not for you to display how to complain on our behalf.
"Please refrain from handing out (the leaflets) or I will escalate (the matter) with ministers who are likely to take a very dim view. I know there are copies in the hall and your troops are ready with them."
Owen also told BAA to prevent passengers taking pictures in the arrivals hall. Pictures of lengthy queues have been posted on Twitter by frustrated people.
Former transport minister Jim Fitzpatrick, Labour's aviation spokesman, said: "This is a pure cover-up. I can understand people wanting to take pictures of the queues. This is further evidence of Border Force trying to hide the severity of the problem.
"Passengers need to know how to register complaints and for Border Force to try to prevent them doing so is outrageous."
The latest row over delays at Heathrow comes as Immigration Minister Damian Green is to be grilled by the Home Affairs Select Committee about the situation.
Committee chairman Keith Vaz said there was "a real problem".
"I'm not saying we should abandon checks but it's a choice for the Government - you either look at the way you deal with people when they arrive at Heathrow or you recruit more staff," he said.
In a joint statement issued tonight, the Border Force and BAA said: "The majority of passengers pass through immigration control quickly but there are sometimes delays at airports for a range of reasons. We think it's important passengers are given the full picture.
"We will not compromise border security but we will work together to keep delays to a minimum."
Shadow immigration minister Chris Bryant said: "The Government is in danger of scoring an extraordinary double own goal,
undermining our border security and giving a chaotic first impression of the UK.
"No airport in the world is designed to keep thousands of people waiting to get through passport control. (Home Secretary) Theresa May and Damian Green need urgently to make resources available so that the events of this week are not repeated.
"The Home Secretary needs to be open and honest with the public and tell us how she intends to resolve these issues now rather than stopping BAA from distributing leaflets. She needs to avoid chaos at our borders come the Summer, the Olympic Games and thereafter."Suggest a correction