Mr Key and Mr Cameron met at 10 Downing Street in London overnight soon after Mr Key arrived from New Zealand.
One of his goals was to try to persuade Mr Cameron to lift new restrictions on visas for skilled job hunters from New Zealand.
Mr Cameron's government is aiming to reduce net migration to below 100,000 at a time of increased migration from the European Union.
Visa restrictions have more than halved the number of New Zealanders moving to Britain for work to about 350 a year. Those restrictions require people to have a job in the UK before securing a visa.
Mr Key said he and Mr Cameron agreed people-to-people links helped sustain and keep vibrant the relationship between the two countries.
"In that context, I outlined New Zealand's continued concerns over immigration restrictions and the air passenger duty tax."
However, after the meeting he acknowledged any changes were unlikely.
Mr Key did, however, have some high-level support for his quest from London Mayor Boris Johnson, who Mr Key met after seeing Mr Cameron.
After that meeting, Mr Johnson said he supported free labour exchanges between the UK, Australia and New Zealand.
Mr Key said New Zealand's priority would now be ensuring that the remaining travel and work rights were not diluted further - including the working holidays 'youth mobility' scheme and ancestry visas for those with British grandparents.
"It's a very tricky situation for [Mr Cameron]. At the end of the day, immigration is a big issue here. With their position with Europe they have enormous numbers of people who can freely and as of right come to the UK and that is putting stress on their system. So we have to acknowledge that."
The restrictions, put in place in 2010, have meant the number of skilled migrants going to the UK has almost halved and Mr Key has described restrictions as "grossly unfair".
Mr Key said the changes meant it was almost impossible for someone to get a job in the UK from overseas, because UK employers are also required to prove that they can not recruit someone in the UK itself and the wider EU first. However, he acknowledged changes in New Zealand's favour were unlikely because of the influx from the EU.
Mr Key said other than the immigration niggles and a hefty $190 departure tax on passengers to New Zealand which he said was driving down tourist numbers, the relationship with Britain was strong.
A Free Trade deal with the EU?
Mr Key also pushed New Zealand's case to begin free trade talks with the EU with Mr Cameron. New Zealand is one of only about five trading countries which has not begun trade talks with the EU, partly because the EU has been bogged down in negotiations with others.
Mr Key said the United Kingdom could help break that stalling pattern because it was a economically powerful member of the EU. Although Mr Cameron plans to hold a referendum on Britain's part in the EU soon, Mr Key said his support for free trade talks would still carry some weight.
"They are an important member of the EU and any help they can give us to advance that would be really useful."
He would also raise it with French President Francois Hollande who he is due to meet next week.
Britain remains one of New Zealand's largest trading partners, with two-way trade totalling NZ$2.5 billion in the past year. It is a key destination for exports and the largest source of international visitors and foreign investment.
Mr Key said the UK was focused on opportunities for closer engagement in the region, which New Zealand saw as another thread to its relationship with the UK and Europe.
"We also discussed how we could work together to develop opportunities in the Asia Pacific region."
Mr Key and Mr Cameron also discussed New Zealand's bid for a Security Council seat in 2015 and Mr Key said he was hopeful of the UK's backing, although as a permanent member it was unlikely to publicly state it.
The pair also spoke about the centenary of the start of World War I for which numerous commemorations are planned - it was the first issue Mr Cameron raised, including New Zealand's part in Gallipoli, as the pair chatted before the closed-doors meeting began.
Mr Key said later that the war had helped forge the modern relationship with the United Kingdom.
"That is not something we take for granted.
"In commemorating our shared past, Mr Cameron and I both agreed we should take every opportunity to ensure the relationship remains relevant and continues to grow and develop."
Syria
After talks with Mr Cameron and British Foreign secretary William Hague, Mr Key said New Zealand might offer up any expertise it had dealing with chemical weapons if things progressed in Syria.
"In the end it will be a solution the UN will be involved in and New Zealand might, if requested, add support. Anything that can make sure that the people of Syria are never subjected to chemical warfare again is really important."
He said there were high hopes the Russia solution for Syria would come to fruition and Syria would give up its chemical weapons to the international community.
"That would be a tremendous step for the people of Syria. We acknowledge the challenges in having that achieved, but it is a very sensible step forward."
He said there was naturally some scepticism about Syria's response.
"But what are the other alternatives? None of them are terribly attractive."
New Zealand agreed to the UK's request to formally express its intention to join the Open Government Partnership (OGP) later this year.
The UK is the current co-chair of the OGP - a group of 58 countries and nine civil society organisations committed to transparent and open government, combating corruption, and harnessing new technologies.
- By Claire Trevett of the NZ Herald/additional reporting APNZ
