Prime Minister John Key and his wife Bronagh joined a private family celebration with British Prime Minister David Cameron at Chequers retreat a few hours ago before the two leaders had talks at the start of a visit.

Mr Key told the New Zealand Herald that Mr Cameron's daughter Nancy turns 11 tomorrow and her parents put on a birthday lunch at Chequers, the official country retreat of the British Prime Minister, with extended family and friends.

Mr and Mrs Key were also invited to plant an oak tree on the estate, as is customary for visiting leaders.

Mr Key and Mr Cameron talked about New Zealand's potential contribution to the fight against Isis in Iraq but Mr Key said a decision was not imminent.

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"There has been a bit of back and forth in terms of scoping out the location and until we can really get a sense of that and what sort of contribution is required and ourselves assess the risk, we are not in a position to say yes or no," he said.

"If we are going to make the decision to do it, the decision has to made in the next month to six weeks but it is not something we will be making at the first cabinet [Tuesday next week] or anything like that." A "more realistic" timetable would be about mid February.

Mr Key and Mr Cameron also discussed the heightened terrorist threat in Europe and the attacks in Paris in which 17 people were killed.

"In some sense nothing has changed. All of us have believed there is that sort of risk that presents itself now and that is consistent with what we see.

"In the end there are a small group of very disaffected people who are basically fanatical.

"In a lot of ways it is terrifying what took place in Paris but it is something we always knew was potentially possible."

The risk of such attacks was more pronounced in other countries "but they are also a possibility in a country like New Zealand -- it is just a lower risk environment." He said that in terms of the Cricket World Cup which New Zealand is co-hosting in February, there were no specific threats but there was consistent advice that hosting international events of the scale of the Cricket World Cup or the G20 presented higher risk.

Mr and Mrs Key went straight from their holiday home in Hawaii to Britain, staying with friends in Norfolk before arriving at Chequers about midday and leaving about 3.30 pm.

He will meet business leaders and the Governor of the Bank of England, Mark Carney, and visit the Imperial War Museum.

Mr Key will chair a meeting in Bosnia and Herzegovina of centre right parties belonging to the International Democratic Union before heading to the Davos alpine retreat in Switzerland to attend the annual World Economic Forum.

The meeting is set to draw more media coverage than usual with Prince Andrew reportedly contemplating making a statement at a reception there he is due to attend about allegations of sex with an underage girl.

Commenting on the resignation of GCSB spy chief Ian Fletcher which was announced last week, Mr Key said the reasons for Mr Fletcher's departure were genuinely around "a family matter."

"I can't go into the specifics of that but it is genuine." He believed Mr Fletcher had done a very good job.

"The suggestion that somehow there is rift between him and the Government or there is a merger with the SIS and GCSB that's imminent or he doesn't agree with the review that's about to take place is not true."