Judges expelling migrants from Britain feel they can make little difference because too many are not being sent home, MPs have been told.
Visa applications have risen over recent months
The fears were voiced by Mr Justice Hodge, head of the board which judges appeals on immigration decisions.
He said removing people was a "big, big problem" for the system.
And he said the government had underestimated the backlog in appeals, with 12,000 more found in "cupboards" than previously thought.
The Conservatives say the system is suffering from the government's lack of competence.
Ministers have instead highlighted moves designed to cut the backlogs.
Mr Justice Hodge appeared before the home affairs committee with leading High Court judge Mr Justice Collins.
Conservative MP Richard Benyon asked whether the volume of cases could be substantially reduced if there was an efficient removals system.
Mr Justice Hodge said asylum claims had dropped across western Europe.
But on immigration cases, he said: "One of my judiciary's concerns always is we work hard to produce a result and it does not result in anything very much.
"Members of Parliament probably feel exactly the same and so does the Daily Mail and other worthy journals... An efficient removals system would be great."
The Home Office and Foreign Office should together redouble efforts to persuade other countries to take back migrants, he said.
And he argued that if people found to be in the UK wrongly were likely to be sent home it would reduce the incentive to come to Britain in the first place.
Mr Justice Collins said delays in removing people caused problems in judicial review cases.
"But I don't underestimate the case for removal," he added.
As well as persuading other countries, there were also nations, such as Zimbabwe, where it was not safe to return people, even if their asylum claims had failed, he said.
The Home Office website shows that 56,290 people were removed, or left the UK voluntarily, last year.
But a spokeswoman said the Home Office did not publish statistics on how many people's removal was pending.
On asylum alone, the government last year missed its target for the removing more failed asylum seekers than the number of unfounded claimants arriving.
It said it needed until February this year to meet the target.
After the committee hearing, Sir Andrew Green, from Migration Watch UK, said removals were the key to the whole asylum system.
Citing historical figures, he said: "With only one in five failed cases being removed, the law is being brought into disrepute and a great deal of taxpayers' money is being wasted."
The home affairs committee is looking into the immigration and asylum system.
Mr Justice Hodge said his tribunal was working to clear a backlog of 22,000 cases.
The number of cases. especially on entry visas, had increased "massively" over the past nine months, he said.
The backlog had been caused by "policy people" underestimating the numbers and by more appeals being found in the "cupboards".
The Home Office had estimated there were 30,000 outstanding appeals when there were 42,000, he said.
Mr Justice Hodge also said there was no record of people visiting Britain leaving the country.
"In public policy terms, if there was a record of people leaving the country... then it would be much clearer about what you might do about it," he said, accepting this would come at great expense.
The judge said initial decisions on asylum cases had "improved substantially" since 2001.
But the work of entry clearance officers, who handled visa applications, was not as good.
He suggested the officers could benefit from extra training.
And when their decisions were overturned by judges, they should be sent details of the judgements so they could learn from them - something he was surprised did not already happen.
The Asylum and Immigration Tribunal was set up in to streamline the process so only one appeal was allowed against Home Office decisions.
Mr Justice Collins said the system had failed to do that. More expensive judicial reviews had simply become the new second tier of appeals.
But Mr Justice Hodge disagreed, saying the number of appeals had fallen under the new system and they were being deal more quickly.