Last year, more than 4000 New Zealanders entered Britain that way, he said.
Under the mobility scheme, 12,000 New Zealanders a year aged 18 to 30 could work for two years.
New Zealanders visiting for less than six months required no visa.
"Along with Australia and Canada, New Zealand has more visa and non-visa routes than any country into the UK outside the UE," he said.
Mr Sinclair said the purpose of the skills charge on employers was to incentivise British employers to invest in training the UK resident workforce and reduce reliance on migrant labour.
"The UK benefits from immigration and is open for business," he said. "Migrant workers fill skills gaps and help boost our economy, but it is right that UK employers look first to the resident workforce."