Unions representing border guards have announced that immigration staff will strike for a day on 10 May.
The chaos and lengthy queues that have blighted Heathrow in recent weeks could worsen to the point of travellers waiting up to four hours to get through passport checkpoints.
Around 4,600 immigration officials are thought to be involved in the strike, and Home Office officials have drawn up plans to get Military Police and civil servants to man desks for the day, according to the report in the Telegraph.
Although the Government said disruption would be "minimal", one union representing border staff pointed out that anyone drafted into to cover would take longer to process passengers.
Lucy Moreton, the Immigration Services Union's (ISU) deputy general secretary, said that disruption next week was almost a sure thing: "I would be amazed if we didn't see queues of up to four hours at Heathrow," she said.
"Last time the Home Office threw a large number of managers at it and the airlines co-operated by encouraging passengers to travel on another day.
"Unless they do the same things again there could be really serious problems."
The unions have voted to strike over pension reforms that will mean employees will work for longer, but receive less upon retirement.
Immigration chaos spreads from Heathrow to Eurotunnel
Passengers face paying for passports to be checked
Sign up to our weekly newsletter | Follow us on Twitter | Become a fan on Facebook