Chair of the Home Affairs Select Committee Keith Vaz says staff must forgo any bonuses until the backlog is sorted.
Immigration Minister Mark Harper has said the increase in the number of outstanding immigration and asylum cases raises "legitimate concerns".
In a statement, he said:
Keith Vaz, the Commons Home Affairs Select Committee Chairman, has said the backlog of outstanding immigration and asylum cases is "spiralling out of control".
In a statement, he said: "There are now about the same number of cases awaiting resolution by UKBA as there are people living in Iceland. The backlog is spiralling out of control."
MPs in the committee added: "We are concerned that the closure of the controlled archives may result in a significant number of people being granted effective amnesty in the United Kingdom, irrespective of the merits of their case.
"For this reason we are concerned that the final checks made on these cases should be thorough and that they should not be rushed to meet an artificial deadline.
"We are particularly interested to find out whether any such individuals would be offered an amnesty or if they would have to start their asylum or immigration application again."
The Home Affairs Committee completes quarterly inquiries into the work of the UK Border Agency and its latest report, which covers the second quarter of the year from April – June 2012, has looked at the number of backlog cases the agency is dealing with.
The troubled agency had 302,064 cases to investigate, trace or conclude by the end of June - more than 25,000 compared with the end of March, figures showed.
Most of the increase came from a rise of more than 24,000 missing migrants who have been refused permission to stay in the UK but whose whereabouts are unknown, referred to as the migration refusal pool.
The number of outstanding immigration and asylum cases rose by 25,000 in three months and is "spiralling out of control", making the total caseload the equivalent of the population of Iceland, the Commons Home Affairs Select Committee Chairman Keith Vaz has said.
More than 300,000 cases needed to be dealt with at the end of June, up 9% over the previous three months, the Commons Home Affairs Select Committee revealed.
But clearing the backlog should not be a rushed job done without the proper checks, the committee's report on the UK Border Agency (UKBA) warned.
Australia's Prime Minister Julia Gillard said that "most" of the people on the asylum boat that capsized early this morning near Christmas Island in the North West of the country have been rescued.
Imprecise numbers for the boat's occupants mean they could not say if anyone was missing at this stage.
A boat believed to be carrying 150 asylum seekers has capsized off the coast of North West Australia. A spokeswoman for the Australian Maritime Safety Authority said:
"A vessel has capsized 107 nautical miles north of Christmas Island, there are reportedly 150 people on board. We don't have numbers on survivors at this stage."
The capsize is the latest in a series of refugee boat disasters in recent years, as rickety, overloaded vessels packed with desperate migrants struggle to reach Australia.
A boat carrying around 150 people has capsized 107 miles off the North West coast of Australia.
Two merchant vessels are on site and more vessels and aircraft were on the way to the scene, a Customs spokesman from Australia's Customs and Border Protection said.
The incident is the second in a week: last Friday, a boat carrying around 200 suspected asylum seekers capsized between Indonesia and Australia, claiming around 90 lives.
Almost half of women seeking asylum in Britain have fallen victim to rape in their home countries, according to a report published by a refugee support group.
Women For Refugee Women said its report into the fate of more than 70 respondents living in seven UK cities also found that the vast majority claiming to have been raped had been refused asylum.
Of those refused asylum, two-thirds were left destitute - with no support or housing - and more than half had thought about killing themselves.
- 48% of those questioned had experienced rape as part of the persecution they were fleeing.
- 56% of women refused asylum said they had been forced to sleep rough in Britain.