An amnesty for an estimated 618,000 ­illegal immigrants in Britain would provide a £3bn boost to the economy, ­according to a London School of Economics study commissioned by the London mayor, Boris Johnson. The study, published last night by the London assembly, dismisses fears that an amnesty would trigger ­further large-scale illegal migration, arguing that ­Britain's border controls would be an effective deterrent.

"So, far from a financial burden, as some suggest, this new research has found an amnesty could be worth up to £3bn a year to the country's economy," the study said. Johnson welcomed the report, saying it had introduced some hard evidence and academic rigour into a debate dominated for too long by myth and anecdote.

The research estimated there are 618,000 illegal migrants in Britain, with more than two-thirds, 442,000, in ­London. But if their position was ­regularised, £846m a year would be raised in taxes. The short-term public sector costs of giving them indefinite leave to remain in Britain at about £410m a year, according to the study, rising to a possible £1bn a year in the long term if they received welfare benefits and public sector housing.

The study found that about two-thirds of those living in Britain as illegal migrants would be eligible for an amnesty which granted legal status to those who have been resident for at least five years as part of a regularisation programme. The detailed estimates suggest that regularisation could raise an individual's earnings by 25% and employment rates by 6%, and imply an additional £3bn a year boost to national gross domestic product.

Johnson first called for an amnesty for long-term migrants last April. It provoked accusations of naivety from Phil Woolas, the immigration minister, and claims that it would lead to more people-trafficking.

The study says amnesties and regularisation programmes have been common in many countries in recent years, including the US, France, Spain, Italy and Greece.

The LSE research came as a Commons public accounts committee report showed it would be at least another four years before the UK Border Agency reached its "optimum capacity" to remove failed ­asylum seekers.

Only 12,000 were removed last year. The MPs' report said Home Office staff on asylum cases are still using fax machines, paper files and handwritten interview notes and will not have a better IT system until 2013. It will also take four years to expand the availability of detention spaces to the 4,000 needed to step up the pace of removals.

The Home Office told the MPs that it was on track to finish working through the backlog of 400,000 to 450,000 cases, some of which date back years. The backlog will finally be cleared by 2011.

Edward Leigh, chairman of the public accounts committee, said: "The process of coming to decisions on whether to grant asylum is still too slow."