Passengers at Stansted Airport faced "unacceptably long" immigration queues at the beginning of the Bank Holiday weekend.
Hundreds of disgruntled passengers were delayed for up to two hours at passport control at the Essex airport yesterday evening.
A spokesman for Stansted airport said action was needed to address the issue of long waits urgently.
He said: "The majority of passengers arriving at Stansted pass through border controls quickly and securely. However, at peak times, and similar to many other UK airports, immigration queues can be unacceptably long.
"We recognise that maintaining strong border security is a priority but we also want to see sufficient resources available to meet passenger demand and keep delays to a minimum at the busiest times.
"Our customer service teams work closely with the UK Border Force to help manage queues and assist passengers at peak times but we believe further action is needed to address the issue as a matter of urgency."
One passenger told the BBC she waited for two hours at passport control, another said after a flight from Cork she waited so long they were put into another area.
Other passengers expressed their frustration on Twitter. Sophie Elliot today posted on the social networking site: "Last night at Stansted we were trapped in queues of over an hour - longer for the people behind us - cos 'a few planes landed early'."
A Border Force spokesman said: "We flexibly deploy staff to meet demand, meaning that the vast majority of passengers pass through immigration controls quickly.
"We will not compromise border security but work closely with airport operators to keep delays to a minimum."
The Government has already admitted there is a "problem" with delays at passport control at Heathrow airport.
As the row grew over the impact of lengthy queues on the UK's reputation and ability to deal with the 2012 Olympics, Immigration Minister Damian Green said he accepted that some passengers had been forced to stand in line for up to 90 minutes in breach of Border Force targets and pledged action to tackle the problem.
Shadow Home Secretary Yvette Cooper called on Mrs May to "get a grip".
She said: "So much for the Prime Minister ordering Theresa May to get a grip last week. The chaos at our borders is clearly spreading to port after port - damaging our global reputation and our security too.
"This is becoming a circus, with staff being shunted from port to port to try and keep up because they cut so many in the first place without a back-up plan.
"She needs to get a grip, sort out unacceptable delays at our borders and make sure their are enough officers available at all our ports to maintain security too."