One in six foreign offenders living in the community have absconded, including 58 dangerous individuals who have been missing since 2010, the National Audit Office has revealed.

The NAO also found that police were failing to conduct overseas criminal record checks on more than two-thirds of arrested foreign nationals.

The spending watchdog discovered the failings despite successive governments throwing resources at the problem of monitoring, arresting, prosecuting and deporting foreign-national offenders (FNOs). Auditors found there were now 10 times the number of staff employed on the issue than there were in 2006.

But far from deterring or speeding up the deportation of prisoners, the number of FNOs either in prison or deported has remained broadly unchanged.

The report will increase scrutiny of the home secretary, Theresa May, who will be well aware that the Labour home secretary Charles Clarke was forced to resign in 2006 after neglecting the management of FNOs.

May has been under pressure from Ukip and Labour over the effectiveness of police background checks following the case of the late Arnis Zalkalns, the prime suspect in the murder of schoolgirl Alice Gross. He had served seven years for murder in his native Latvia.

In 2011, David Cameron pledged to deport more FNOs, revealing plans to remove those who are given indeterminate sentences as soon as they have served their minimum jail term.

The report found public bodies spent an estimated £850m on foreign criminals, although the figure could be as high as £1bn, which it said equated to roughly £70,000 a year per criminal.

There were 12,500 FNOs in Britain at the end of March this year, either in prison or living in the community pending deportation.

The government has made little progress on the issue since 2006, the NAO said. Foreign prisoner numbers have risen 4% from 10,231 to 10,649 since 2006, while removals have fallen to 5,097 from a peak of 5,613 in 2008/09. This comes despite an increase in the number of Home Office staff working on FNOs from 100 to more than 900.

Despite the 2006 crisis, the NAO discovered the Home Office does not hold records on the number of foreign offenders released without being considered for deportation before January 2009.

Teams set up to manage foreign offenders still use old technology with referrals from the Prison Service being sent to the Home Office by fax and manually entered into the records system.

At the border, the UK is also lagging behind its European counterparts in preventing foreign criminals from entering the country, the report shows.

Britain is one of four countries in the European Economic Area, of which there are 30 member states, not to sign up to the Schengen Information System, which uses warning alerts about foreign nationals.

Up to £70m a year could be saved if early opportunities to identify foreign national offenders were seized upon, auditors said.

In 2013, the National Security Council realised more could be done and ordered the Home Office, Ministry of Justice and Foreign and Commonwealth Office (FCO) to step up efforts, auditors said. In June 2013, the three departments established the “FNO action plan”.

The report discloses the case of a foreign offender who has been jailed twice for sexual offences, including assaulting a girl under 14, but remains in the UK despite a near eight-year battle to deport him.

The man, who arrived in the UK as a student in 1980, was granted indefinite leave to remain in the UK in 2005 – despite being jailed for three counts of indecent assault of a female under 14 five years earlier in 2000.

But it was not until 2007, when he was serving a second jail sentence for indecent exposure, that the Home Office first told the man of its intention to deport him, the report says.

David Hanson, shadow immigration minister, said the report showed the coalition’s immigration policy was not working. “How can it be that after five years in office David Cameron’s government are deporting over 500 fewer people than in 2010?

“Labour has warned the government that their failure will undermine public trust in the immigration system and cost the taxpayer money. We have set out clear plans to make it easier to deport foreign criminals. It is time for the government to rethink its approach and for David Cameron to make good on his promises.”

Margaret Hodge, chair of the public accounts committee, said the government’s performance in reducing the number of foreign national prisoners continued to be “frustratingly poor”.

“It beggars belief that the Home Office and Ministry of Justice are managing the removal of foreign national offenders without knowing basic costs and how best to target their resources.

“Government is not helping itself – continued use of outdated IT and too much reliance on form-filling mean that crucial checks and information gathering are not happening at the right time.

“Given its poor track record, government will need to make huge strides to improve its management of foreign national offenders through its still-evolving 2013 cross-government action plan.”