Heathrow airport has been ordered to stop handing out leaflets to passengers that apologise for delays at immigration.
Marc Owen, director of UK Border Agency operations at Heathrow, also told BAA, the airport's operator, to stop passengers taking photos of long queues.
The attempt to play down increasing anger at the length of queues for travellers arriving at border control has been labelled a "cover-up" by one MP.
In an email obtained by The Daily Telegraph, Mr Owen said the leaflets – which explain how people can complain to the Home Office – were "inflammatory and likely to increase tensions in arrivals halls".
He said: "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."
Mr Owen also told BAA to prevent passengers taking pictures in the arrivals hall. Pictures of lengthy queues have been posted on Twitter.
Former Transport Minister Jim Fitzpatrick, Labour's aviation spokesman, said: "This is a pure cover-up. Passengers need to know how to register complaints and for Border Force to try to prevent them doing so is outrageous."