Delays at Heathrow Airport passport control left passengers queuing for up to two and a half hours last month, figures show.
On 30 of 31 days in July, Border Force missed its target of a 45-minute wait or less for 95% of visitors from outside the European Economic Area.
Virgin Atlantic, which obtained the data, said passengers were "frustrated".
The government said it would send 200 extra staff to Heathrow this summer.
According to the data, the longest immigration queues were on 6 July when travellers from outside the European Economic Area (EEA) - an area made up of 31 European countries - had to wait in line for up to two hours and 38 minutes.
Craig Kreeger, the boss of Virgin Atlantic, said while it was agreed that security and safety was a priority, other countries were managing their borders better than the UK.
He said "only the Border Force" could take action to "resolve these unacceptable queue times".
"At a time when the UK needs to show the world it is open for business, the government and Border Force need to provide a great first impression for every visitor every time," he said.
Citizens aged 12 or over from the European Union, the EEA and Switzerland can use the electronic gates at Heathrow's passport control - but visitors from all other countries must have their passports checked by a Border Force official.
Michael Klein, an art dealer from New York who regularly travels through Heathrow, described his experiences of the airport as "just horrendous".
Mr Klein, 66, told the BBC he had queued for two hours or more at passport control on three occasions in the past month alone.
"There's absolutely no accommodations made for families or elderly. No one seems to care," he added.
John Holland-Kaye, Heathrow's chief executive, has previously called for the Home Office to allow visitors from "low risk countries" - like the US, he suggests - to be allowed to use the electronic gates.
Last week the boss of British Airways, Alex Cruz, wrote a letter to the Times urging the government to deal with Heathrow's "border farce".
He said "two-hour queues are fast becoming the norm" and Heathrow had missed its target for non-EEA arrivals 6,000 times so far this year.
BBC reporter Jenny Kumah said the Home Office explained its poor performance in July was worsened by a "large numbers of vulnerable adults and children arriving", alongside a number of computer errors.
A Home Office spokesman said: "The vast majority of people who arrive at Heathrow get through the border within our service standards.
"But we understand the frustration for those who have experienced longer waits and remain fully committed to working with our partners to reduce waiting times as far as is possible.
"At the same time, we will not compromise the essential checks we carry out at the border which keep our country safe.
"We are making sure Border Force has the resources it needs and are deploying 200 additional staff at Heathrow over the summer."