Ministers say the UK's borders have never been more secure
MPs have criticised bonuses totalling £295,000 paid to 29 UK Border Agency officials last year, saying it was still clearly under-performing.
UK Border Agency documents show a raft of cases where there is "no formal record" of applicants having left the UK, the Home Affairs Committee found.
The MPs said a 2011 target for clearing its case backlog must be accelerated.
Ministers said there had been major improvements to procedures and bonuses were paid only for outstanding work.
The UK Border Agency has been working to clear a backlog of asylum cases stretching back many years.
It was reported in October that 40,000 asylum cases may effectively be abandoned and applicants allowed to remain in the UK because it was too difficult to return them to their home countries.
At the time, ministers denied this amounted to an effective amnesty, stressing that individual applications would continue to be assessed on their merits and no illegal immigrants would be allowed to stay.
The cross-party committee said it was "astonishing" these cases, some of them six years old, were classified as "abandoned incomplete" with no record of whether applicants had been granted leave to remain or refused permission.
"What is really surprising and disappointing is the number of cases where the Border Agency is basically saying 'we don't know' exactly what has happened to these applicants," said the committee's chairman, Labour MP Keith Vaz.
"Over half the applications are concluded for some 'other' reason than being granted or denied leave."
Immigration Minister Phil Woolas defended the bonuses, saying they were necessary to recruit and hold on to quality staff from the private sector.
He said: "With the creation of the UK Border Agency we assembled a management team from across Whitehall and beyond who are leading dynamic changes across the business.
"I believe that it is right to reward staff for outstanding work, and bonuses are only ever awarded to those who have performed to a high standard."
According to the report, of the 450,000 cases outstanding in 2006, 220,000 have since been dealt with - a reflection, MPs say, of the increased resources given to the Border Agency.
Within this, about 74,000 asylum seekers have been permitted to remain in the UK while 30,000 have been deported, it said.
But the committee suggests there were errors in 88,500 of the cases reported to have been concluded.
It is calling on the Home Office to bring forward its deadline for clearing all cases from 2011 to September 2010, saying "it simply must get through them faster than promised".
The committee is taking issue with the fact Border Agency officials were paid a total of £295,000 in bonuses last year despite the unresolved problems.
Although the agency had made progress in recent years, Mr Vaz described the payouts as "astonishing".
"We know it has had a lot to contend with but it is apparent that it still has a long way to go before it is operating as it should," he said.
Ministers said the Border Agency had made "considerable improvements" in recent years, thanks to the introduction of the new points-based system for migration - backed by the Home Affairs Committee earlier this year - biometric visas and ID cards for foreign nationals.
"The truth is that our border has never been stronger, as illustrated by the fall in asylum applications, the record numbers we are stopping at Calais and the watch-list checks that are undertaken before people even step on a place," immigration minister Phil Woolas said.
It was right that those responsible for "dynamic changes" at the organisation were rewarded, he added, stressing that bonuses were paid only to those performing "to a high standard".
But the Conservatives said the report was "further confirmation" that the immigration system was still chaotic.
This report makes it clear how far the UK Border Agency has got to travel before we have an immigration system that is firm but fair
Lib Dem home affairs spokesman
"Ministers have had years to deal with the backlog created by the collapse of controls after 1997 but it is clear that they have not succeeded," said shadow immigration minister Damian Green.
"They should treat this as an urgent priority."
The Lib Dems said the Home Office should be stripped of responsibility for the asylum process and it should be given to an independent body.
"This report makes it clear how far the UK Border Agency has got to travel before we have an immigration system that is firm but fair," said its home affairs spokesman Chris Huhne.
Immigration to the UK continued to rise last year, according to official figures published last month.
About 590,000 people came to live in Britain in 2008, compared with 574,000 the year before, figures showed.
But a growing number of people have been leaving the UK permanently.