The UK Border Agency is still failing in its "basic functions" in spite of efforts to overhaul it, MPs have said.
The home affairs committee said UKBA had provided "inconsistent" information about immigration and asylum cases dating back to 2006 and this backlog would take four more years to clear.
It also said it was "deeply concerned" about the number of foreign prisoners living in the UK awaiting deportation.
Immigration minister Damian Green said "past mistakes" were being dealt with.
The UK Border Agency - responsible for securing the UK border at air, rail and sea ports and migration controls - was set up in 2008, two years after then Labour Home Secretary John Reid said the Home Office's immigration directorate was "not fit for purpose".
His predecessor, Charles Clarke, was sacked after it emerged 1,013 foreign nationals had been released from prison, without being considered for deportation.
But the committee's report said, six years on, only 397 of them had been removed or deported - 57 have not been located at all.
The organisation is now being split in two in the wake of a row last year over revelations that hundreds of thousands of people were let into the country without complete checks.
The UK Border Force, the section of the agency that manages entry to the UK, is to become a separate law-enforcement body reporting directly to the Home Office while the UKBA will be solely responsible for immigration policy work.
In its latest report on the workings of the UKBA between August and November 2011, the cross-party committee suggested the agency was also still not getting a grip on the backlog of approximately 450,000 asylum and immigration cases which emerged in 2006.
Last year UKBA officials said of about 365,000 cases where the individuals could be traced, 18,000 remained unresolved.
But the committee said new evidence it had seen suggested the UKBA was dealing with 1,500 more "live cases" than previously indicated. It called on the agency to "clean up and clarify" the figures.
"The agency must rid itself of its bunker mentality and focus on ensuring that Parliament and the public understands its work," the MPs said.
"Confusion over figures only risks suspicion that the agency is attempting to mislead Parliament and the public over its performance and effectiveness."
There are currently 119,000 asylum and migration cases where individuals cannot be located. MPs said, at the current rate of progress, this would take four years to clear.
The committee said it was also taking too long to consider whether foreign criminals could be deported at the end of their prison sentences.
It welcomed the fact that fewer prisoners were being released without being referred for possible deportation, but said there were 3,940 former foreign inmates living in the community - 2,670 of whom were still awaiting deportation after two years.
Rob Whiteman, head of the UKBA, told the committee that the main problems were that some prisoners gave a false identify, so it was difficult to work out where they came from, while others did not have the travel documents needed to be readmitted to their country.
The committee's chairman Keith Vaz said more needed to be done to tackle those obstacles: "The reputation of the Home Office and, by extension, the UK government is being tarnished by the inability of the UK Border Agency to fulfil its basic functions."
He said UKBA "appears unable to focus on its key task of tracking and removing illegal immigrants, overstayers or bogus students" and, having spent £9.1m on iris scanners at airports, had now opted to remove them.
"That £9.1m could have been spent on having immigration officers and case workers that would have cleared the backlog that this committee has been talking about for the last five years."
Immigration Minister Mr Green told BBC Radio 4's Today programme the UKBA had improved from a state of "complete chaos" when the government took office.
"The asylum service is immeasurably much better than it was three or four years ago," he said - with more than 60% of asylum applicants now getting an answer within 30 days, rather than waiting "many years".
"We start deportation action on foreign national prisoners now 18 months before the end of their sentence.
"As a result of that, last year we removed over 4,500 foreign criminals, and 45% of those were by the end of their sentence."
Mr Green said the government had to "clear up the mistakes of the past" in dealing with foreign criminals.
He said the system was still not "perfect" but more would be done to tackle delays to deportation in the coming months, by changing immigration laws to cut "abuse of the Human Rights Act".
Labour's immigration spokesman Chris Bryant said his party had got things wrong during its time in office and should have introduced a points-based system for skilled migrants from outside the EU much sooner.
But he told the BBC the coalition had engaged in"very strong rhetoric about what it was going to do on immigration".
"No politician engaging in what is a very sensitive debate, should be engaging in rash promises. And that is what the government is continuing to do," he said.