The UK Border Agency faces a backlog of more than 275,000 failed migrants who need to be removed from Britain, MPs on the home affairs committee have said.
For the first time in their tri-annual report on the agency, MPs collated all categories of cases not yet resolved.
Chairman and Labour MP Keith Vaz said the agency appeared to have "acquired its own Bermuda Triangle".
The Home Office said the report raised "legitimate concerns" about issues it was aware of and was already tackling.
A spokesman said the MPs had also highlighted improvements it had made to tackle "the huge backlog of cases we inherited".
"Over 2,000 overstayers have recently been removed following targeted enforcement activity, foreign national offenders are being removed more quickly and we are performing well against visa processing targets," he said.
Mr Vaz said the backlog of UK Border Agency (UKBA) cases awaiting resolution was "now equivalent to the entire population of Newcastle upon Tyne".
"It's easy to get in, but near impossible to keep track of anyone, let alone get them out," he said.
The committee said it would take the UKBA "years" to clear the backlog and it was concerned the agency might not have enough resources to do so.
The committee said the backlog included:
At least 150,000 migrants who had been refused permission to stay in the UK
21,000 asylum cases
3,900 foreign offenders living in the community
57 foreign criminals released in 2006 without being considered for deportation and who had not yet been traced
80,000 asylum applications and 21,500 immigration cases in the "controlled archive" of cases where the UKBA had lost track of the applicant
MPs said the UKBA "does not have a strong record in deporting foreign national offenders".
It recommended that the agency establish a team to examine why foreign criminals in the community had not been sent home and to ensure they were deported.
MPs also criticised the way border officials responded to tip-offs about suspected illegal immigrants. They said although intelligence reports were assessed quickly very few were acted upon.
Plea by academics
The select committee said the government's plan to reduce by a quarter the 260,000 student visas issued annually would not benefit the UK.
The international student market was worth £7.9bn, MPs said.
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Talented students are welcome in the UK, but we have introduced new powers to toughen up the system”
Home Office spokesman
They recommended that students instead be excluded from net migration figures so that the government could meet Prime Minister David Cameron's pledge to cut net migration from 250,000 to tens of thousands by 2015.
"This will enable the government to encourage students to come to the UK whilst maintaining their position on curbing immigration," Mr Vaz said.
University chancellors and campaigners have called for international students to be classed as temporary migrants so that they are not counted in the figures.
Officials argue that students staying in Britain for longer than a year are not visitors and that their numbers affect public services and infrastructure.
The MPs also recommended that UKBA inspectors stopped announcing their visits to colleges so that "bogus" institutions could be prevented from abusing the immigration system.
Responding to the report's recommendations, the Home Office spokesman said: "Talented students are welcome in the UK, but we have introduced new powers to toughen up the system, keeping out the fraudulent and unqualified while ensuring genuine students continue to benefit from our excellent educational facilities."
The report looked at the UKBA's work between December 2011 and March.
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