New York has a long history as a magnet for the poor and the homeless. Even the famous poem on the Statue of Liberty, addressed to the world's "huddled masses", exhorts: "Send these, the homeless, tempest-tossed to me . . . !"

But now? Not so much.

A New York scheme to send hundreds of homeless people on a one-way ticket out of town has led to more than 550 families relocated since 2007. Under the scheme, initiated by New York's mayor Mike Bloomberg, the city pays for bus and plane tickets, or petrol vouchers, to destinations varying from cities elsewhere within the US mainland to places like South Africa or Puerto Rico.

The scheme is aimed at saving the costs of putting up homeless families in expensive shelters. It only happens if a family can show they have relatives to stay with elsewhere who are willing to look after them. Then New York will stump up the cash and make the arrangements for them to get out of town, often within a few days of agreeing to leave.

The level of help varies. One couple from Michigan were given $400 (£240) in petrol cards so that they could drive home after a failed quest to find New York jobs. Another family of five got free plane tickets to Paris and then free rail tickets when they arrived to get them to the northern French town of Granville.

Though the travel expenses can often cost thousands of dollars, city officials say it is cheaper than housing families in shelters which can cost around $36,000 a year.

However, the plan has stirred up controversy among charity organisations that work with homeless families. Some say the scheme is a welcome addition to the city's armoury of ways of dealing with a chronic homeless problem.

"It is a good plan," said one director at a homeless shelter who did not want to be named. But others say it does little to tackle the real underlying issues of homelessness in the city and the huge lack of affordable housing in a metropolis famed for its sky-high rents and property prices.

One of the plan's critics is Arnold Cohen, chief executive of Partnership for the Homeless. Cohen says the scheme does not have enough interest in seeing whether families sent out of the city become homeless again or even return to New York. As such, Cohen says, it is only dealing with short-term issues and not doing anything to help people properly turn their lives around. "There is no exploration of whether the family members they are sent to have a long-term relationship with them. They may just become homeless again, but in a new city. Or they may come back," he said.

But other homeless advocates have praised the effort to help families that in many ways have become stranded in New York and welcome the help to get back home. "We are in the compassion business and we are seeing families reunited," said James Winans, development director of the famed Bowery Mission in Manhattan.

Despite the scheme, homelessness is likely to remain a major problem in New York especially in the midst of a brutal recession.

The one thing all homeless advocates agree on is a crippling shortage of affordable housing and the need for more employment training so that homeless people can get a home and a job. Only then will the real issues that cause the problem be dealt with. "The programme just shows the huge demand for housing in the city that is currently just so unaffordable," said Josh Lockwood, executive director of Habitat-NYC, the local affiliate of Habitat for Humanity International.

The closest British equivalent to the New York scheme was an initiative in London to relocate homeless families to towns with a surplus of homes, such as Huddersfield.

• This article was amended on 30 July 2009 to correct spelling and punctuation in the opening line of poetry.