Foreign travellers are being allowed into Britain, even when there are doubts about their eligibility, Home Office research suggests.
Researchers studied cases at Heathrow and Gatwick
At peak times immigration officers sometimes felt under pressure to let people through unchallenged, it found.
Senior officers at Heathrow and Gatwick airports said they sometimes encouraged staff to grant "borderline" cases.
Shadow Home Secretary David Davis said problems at the Home Office were due to a lack of leadership and funding.
The report looked at more than 6,000 cases handled by immigration officers at Heathrow and Gatwick, who check passports and question new arrivals, before deciding whether to allow them entry to the UK.
But the report found: "At certain times of the day, when a lot of flights come in at the same time, control can become extremely busy.
"If this coincides with staff shortages, immigration officers can feel under intense pressure to deal with passengers more quickly than they would like, and sometimes to let passengers through without making further inquiries."
It added: "Some immigration officers described rare occasions when, due to staff shortages, they had been instructed by chief immigration officers not to hold up any passengers at all."
Chief immigration officers also told researchers they sometimes had to prioritise cases and just let through "the ones that are not as bad as the other ones."
The workload was made harder by the loss of experienced staff and intake of "less qualified recruits".
'Not fit for purpose'
Of the cases examined by researchers, black people were 17 times more likely to be stopped at passport control than white people from the northern hemisphere.
But the report did not find people were being stopped because of the colour of their skin. Immigration officers said they based decisions on nationality and other factors like behaviour.
Mr Davis said the report showed the reason why the Immigration and Nationality Directorate was "not fit for purpose" - words already used Home Secretary John Reid to describe the Home Office - was lack of leadership by ministers.
"If [chancellor] Gordon Brown continues to starve John Reid of revenue to do the job and if John Reid continues to rob one vital sector of the Home Office to pay another, this carousel of catastrophes will continue," he said.
Liberal Democrat home affairs spokesman Nick Clegg said: "Once again the government's tough rhetoric is undermined by its total inability to do basic things like staff immigration points properly."
But a Home Office spokesman said the report was based on "small sample sizes" and frontline border control staff was "at an all time high".
He added: "It is completely wrong to say that the immigration service would not hold up people seeking to enter Britain that they believe may be a risk or who would not comply with immigration controls."
He said everyone from outside the European Economic Area had their passports swiped adding: "We check people based on risk and not on queues".