"Europe is the biggest economy in the world, it's a powerful economy notwithstanding the challenges it's had. And if New Zealand could advance a trade agreement with Europe it would be quite important," he said.
He would make the same point to French President Francois Hollande early next week.
"The impression we've always had from the Europeans is not that the door is closed to us forever - it's just that they've been dealing with other issues."
He said that would be a lengthy process, but the UK's help would be important.
"That's where Britain is a great friend for New Zealand and could be a strong advocate for us."
However, Mr Key's attempts to get Mr Cameron to back down on two other issues appeared to be unsuccessful. One is the steep departure tax of almost $200 a head for those flying from the UK to New Zealand.
Mr Key said visitor numbers from the UK had dropped significantly since the tax was introduced.
While he accepted the tax was a revenue-raising effort during the recession, he said it had also impacted on tourists visiting Britain.
However, Britain's economy is starting to recover, which could result in good news on the tax at some point.
Asked if Mr Cameron had given any indication of his plans, Mr Key said his counterpart was in a difficult position but he believed he had made his point strongly, "so let's see where we go from here".
He said New Zealand was getting more tourists from other areas, which helped fill the gap. However, he sent a warning that it could have an effect on the relationship: "Part of it is wanting to ensure that the relationship, which is so broad and deep, stays intact with the UK and that was really the point we were making."
The other issue he hoped to tackle was changes to the skilled migrants visa, which require New Zealanders to have a job before they can move to the UK. The numbers have more than halved since the requirement was introduced in 2010.
Mr Key had some support on the issue from London Mayor Boris Johnson, who said it was an "oddity" that a country with deep links to the UK such as New Zealand should be treated differently from EU countries.
Mr Johnson said it was politically sensitive, but there was no reason countries such as New Zealand and Australia could not have special agreements for labour mobility.
Mr Key said the main priority was ensuring other rights such as the working holiday scheme for young people and ancestry visas were not affected in the future.
John Key's London diary
• Yesterday: The PM met British counterpart David Cameron. Discussed Syria, visa rules, NZ's bid for a Security Council seat in 2015, the role British construction companies can play in the Christchurch rebuild, and NZ's wish for free trade talks with the European Union.
• Also met Foreign Secretary William Hague, London Mayor Boris Johnson and Commonwealth Secretary Kamalesh Sharma.
• Overnight: Was due to speak at Conservative Party caucus retreat and meet Labour leader Ed Miliband.
• Tomorrow: Will attend tourism functions before travelling up to Balmoral Castle for a weekend at the invitation of the Queen.
