The troubled UK Border Agency faces a backlog of cases equivalent to the population of Newcastle, MPs warn.
Missing foreign criminals, failed asylum seekers, illegal immigrants and others refusing to leave the country make up more than 275,000 cases which the agency still needs to deal with, the Commons Home Affairs Select Committee said.
Keith Vaz, the committee's chairman, said the backlog, which will take years to clear, was unacceptable, adding that the agency seems to have "acquired its own Bermuda triangle".
"It's easy to get in, but near impossible to keep track of anyone, let alone get them out," the Labour MP said.
"This is the first time that the committee has collated all the cases at the UK Border Agency that await resolution. This backlog is now equivalent to the entire population of Newcastle upon Tyne."
The Public and Commercial Services (PCS) union, which represents Home Office staff among others, has voted to strike for 24 hours on Thursday - the day before the official opening of the Olympic Games on 27 July.
The PCS said members would take other forms of industrial action on key dates over the games. Staff involved work for the UK Border Agency, the Identity and Passport Service and the Criminal Records Bureau.
The latest damning report on the agency's work also said the committee did not believe the Government's aim of cutting the 260,000 student visas issued each year by a quarter would benefit the UK.
Students should be excluded from the net migration figures instead, it said.
Britain would then continue to attract international students, a market worth £7.9bn, and still be able to aim to meet Prime Minister David Cameron's pledge to cut net migration from 250,000 to the tens of thousands by 2015, the report said.
Mr Vaz added: "This will enable the Government to encourage students to come to the UK whilst maintaining their position on curbing immigration."
University chancellors and campaigners have urged Mr Cameron to class international students as temporary rather than permanent migrants, removing them from the figures.
But Immigration Minister Damian Green has said students staying for more than a year are not visitors and their numbers affect communities, public services and infrastructure.
Monday's report, looking at the agency's work between December last year and March, also called for the agency to make all its inspections of colleges unannounced, rather than giving them advance notice so key people and documents can be ready.
"If we are to eliminate bogus colleges from the education landscape and employers that abuse the immigration system then visits will have to be unannounced, robust and thorough," it said.
On the backlog, the committee said it included at least 150,000 migrants who have been refused permission to stay in the UK but who may still be in the country illegally, 21,000 asylum cases, and 3,900 foreign offenders living in the community.
A further 57 foreign criminals who were released in 2006 without being considered for deportation have not yet been traced.
And the so-called controlled archive, used for cases where the agency has lost track of the applicant, contains 80,000 asylum applications and 21,500 immigration cases, the report said.
The agency "does not have a strong record in deporting foreign national offenders" and should set up a team to examine why the foreign criminals living in the community had not been deported and then to ensure that they are sent home, the MPs said.
In future, deportation proceedings should begin as soon as a prisoner is sentenced to speed up the process, they added.