A “bribe” to persuade foreign prisoners to leave Britain has been more than tripled to £3,000 per offender by the Government as part of its drive to tackle prison overcrowding.

The enhanced incentive is being offered until the end of next month as the Prison Service struggles with a record jail population.

The revised package was introduced by the Home Office without any publicity or formal announcement last month after prison numbers had soared by more than 2,000 in six weeks.

It is the second time in three months that ministers have quietly increased the incentives package. In November they increased the standard £800 package to £1,500 for a limited period.

Foreign criminals from outside the European Economic Area are able to apply for help with education, training, housing and resettlement of up to £3,000 until the end of April. There are an estimated 11,000 prisoners from outside the UK in jails in England and Wales.

Under the scheme announced by John Reid, when he was Home Secretary in 2006, foreign prisoners are eligible for the £800 reintegration package. In addition all foreign prisoners receive £46 discharge grant on leaving jail. British prisoners are eligible for the discharge grant but not the reintegration package.

Lin Homer, the chief executive of the Border and Immigration Agency, said: “We strongly believe foreign lawbreakers should be sent home at the earliest opportunity. Every day that we can get these individuals out of the country early saves our taxpayers over £100 a night. That’s why we want to use the facilitated returns scheme to get as many foreign criminals out of the UK as possible by extending last year’s scheme to last until April.”

Terry Fullerton, chairman of the Prison Officers’ Association at Holme House jail in Teesside, said: “We had to go to their cells and offer them £3,000 if they were prepared to be repatriated to their own country. That is four times more than the annual pay award we received this year. That sticks in the throat of every prison officer.

“The problem is that we have more prisoners to lock up than we have spaces. We are constantly amazed at the ridiculous things the authorities come out with to try to reduce the numbers in prisons.”

The Home Office defended the decision not to announce publicly the tripling in the value of the package available to foreign offenders. The department said that it was not a new scheme but a time-limited enhancement of a programme that was already up and running and had been successful.

A spokesman was unable to explain why the amount on offer had been tripled if the original scheme and the time-limited increase to £1,500 last year had been a success.

A total of 840 of the 4,200 foreign prisoners deported last year returned home under the scheme. A total of 280 went under the enhanced £1,500 package offered between November and January.

The Home Office said that the £3,000 package would make it easier to return foreign criminals quickly to their home countries. It compared the cost of the package with the estimated cost of £11,000 to make an enforced removal from Britain.

Reintegration assistance is provided in kind when prisoners return to their country of origin. It includes education, accommodation and medical care for those who are eligible.

A Home Office statement said: “We believe this will increase the number of returns we can achieve and also help ensure they occur at an earlier stage in the process.

“We will fingerprint prisoners, exclude them from the country and place them on watch lists to prevent them from returning to the UK after they are removed.”

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