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The "nightmare" story of a British immigrant family to New Zealand is attracting the attention of the UK media and giving New Zealand a bad rap.

Britian's Daily Mail newspaper has published a story titled 'Expats' paradise lost on New Zealand's jobs crisis - just weeks after it was named best place to make a fresh start'.

The story details the Kemp family who came to New Zealand with the promise of work but have since been made redundant.

The British tabloid Sun is also understood to be writing a story on the issue.

The interest was sparked after a story in the New Zealand Herald last Thursday, in which a migrant group said the Government was "taking migrants' money, using their skills and then telling them to bugger off".

Mike Bell, a spokesman for the Move 2 New Zealand Trust, representing mainly migrants from Britain, Europe and South Africa, said thousands of migrants who had moved to New Zealand on the promise of permanent work and residency visas were now being told to "bugger off".

He also said he had invited Immigration Minister Jonathan Coleman to a meeting but had only had an answer from the associate minister which was "less than favourable".

A spokeswoman for Mr Coleman said the minister has "prior commitments and is unable to attend."

Meanwhile Immigration New Zealand has responded to the Daily Mail article.

Immigration service delivery manager Steve Cantlon said the country still has skill shortages in some areas of the economy.

He said claims of an "anti-migrant job crisis" are not founded on facts.

"New Zealand immigration policy has always been based upon ensuring that New Zealanders have the first opportunity to take up work vacancies. This policy has and continues to be reflected in the Government's official skill shortage lists," Mr Cantlon said.

He said a temporary work permit is just that, temporary.

"One can only feel sympathy for the plight of families who have had to return home because of the changing labour market. However temporary workers have always known that there was no certainty that their permits would be extended or that they would be able to progress on to permanent residence," Mr Cantlon said.