New Zealand Prime Minister John Key says he has made "genuine progress" in reforming departure tax, which was one of the big issues he discussed with UK Prime Minister David Cameron at Downing Street in London today.
Mr Key said he had an "invaluable hour and a half" with Mr Cameron over a "relaxing, casual" dinner.
He said the ultimate success of the discussions would be measured by opportunities to resolve issues in the future, rather than any set outcomes this week.
Mr Cameron wanted to reform the departure tax system, so it is "fair for those who want to travel to New Zealand", said Mr Key, who will talk about the issue further with UK Chancellor George Osborne this week.
Mr Cameron offered his condolences and sympathies to the earthquake-hit people of Christchurch and said he had "huge admiration" for their "courage and steel".
New Zealand had the "condolences and sympathy of everyone in Britain", Mr Cameron said and there was "huge admiration for the grit and determination that the people had shown in putting that great city back together".
Mr Key thanked his host for Britain's contribution to the rescue effort.
The prime ministers also spoke about Libya, Afghanistan and the economic situation in both New Zealand and Britain.
Mr Key said Mr Cameron believed he was "absolutely right" to take action in Libya.
The two prime ministers agreed they were "making progress" in Afghanistan "but we are all in agreement that ultimately we want to withdraw our forces there" and provide a stable environment for government.
On the economy, Mr Key said in many respects the economic issues were similar in New Zealand, though on a smaller scale than in the UK.
Mr Key met the Queen for lunch at Windsor before meeting Mr Cameron.
The Queen wanted to pass on her best wishes to the earthquake people of Canterbury and was also "very concerned" about the families of those killed in the Pike River disaster, he said.
He would not reveal what they said about Friday's royal wedding, between the Queen's grandson Prince William, and Kate Middleton.
Mr Key said he had "eaten for New Zealand" on the trip -- poached egg, beef and panna cotta with the Queen, and salmon, lamb, mousse and cheese with Mr Cameron.
Mr Key will visit French leader Nicolas Sarkozy in Paris tomorrow, where Libya and Afghanistan will again be on the agenda.
He said there was "potential" for greater access for free trade between New Zealand and Europe.
He was keen to influence Mr Sarkozy because the French president was chair of G8 and G20 this year. Mr Key said the French and German "powerhouse" economies could be bigger markets for New Zealand exports.
Mr Key also hoped to influence the UK and France into supporting the New Zealand bid for a seat on the United Nations Security Council.
He said the climax of his European trip, the royal wedding, was "very important" to Mr Cameron as a good news story.
He said the two meet "eye-to-eye" on most issues.