Mr Key said Mr Cameron assured him he was "going to go away and have a look at that".
Asked if he had reminded Mr Cameron that New Zealand had voted to keep the Union Jack on its flag, he said: "Good grace stopped me pointing that out."
Britain's big issue was that it had a huge amount of migration, from Europe, that it could not control.
"But we are migrants who have always pulled our weight in the UK and why should we be penalised for the migration policies of being part of Europe?"
The first lot of changes to take effect later this year (no exact date has yet been announced) mean experienced Tier 2 migrants will have to earn $52,000 a year to stay in Britain beyond five years.
From April next year, the threshold will be raised to $63,000.
The earnings threshold for new entrants to the Tier 2 category will remain at $43,000.
From April next year, an annual charge of $2000 will be imposed on employers of Tier 2 visa holders or $760 a year for small and charitable employer sponsors of skilled migrants.
Britain says the reason for the charge is to reduce reliance on migrant workers and encourage British employers to hire locally.
The changes will not affect New Zealanders applying for the youth mobility scheme.
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.
Mr Key and Mr Cameron are in Washington for a Nuclear Security Summit hosted by United States President Barack Obama.