Some of our tourists are missing: more than half the British travellers who went to New Zealand last year failed to return. That is according to official figures; the New Zealand authorities counting them in, and our government counting them home.

Let me explain how I reached that conclusion. On Wednesday it was widely reported that, as a nation, we took 10 million fewer trips abroad. One of the "biggest losers", according to the Office for National Statistics (ONS), was New Zealand, with a 30 per cent fall in British visitors.

Page 59 of Travel Trends 2009 reported that British visits to New Zealand fell from 169,000 to 117,000 last year. Initially, I took the figures on trust. But when an industry contact expressed incredulity at the scale of the slump ascribed to the "Land of the Long White Cloud", I compared UK government figures against other sources. Starting with UK government figures.

"Around 300,000 British people visit New Zealand each year," says the Foreign Office – which does not rely on the ONS, but cites its source as Statistics NZ. The Kiwi bean-counters can be fairly confident about their figures, because every foreigner who arrives by legitimate means – the vast majority by air – has to fill out a form, citing their nationality. So, unless a significant number of people are landing surreptitiously by boat, this small nation with modest tourist numbers knows pretty precisely how many people arrived from Britain last year: 258,438. Yet the ONS, which counts people returning home, says fewer than half that number made it back.

They may still be in New Zealand: working illegally, falling victim to one of the many risks in the outdoor capital of the world, or spirited away by orcs left behind by the makers of The Lord of the Rings. But if one Brit really was leaving every four minutes for New Zealand, and failing to come back, I suspect we might have noticed by now – just as the locals would surely spot an increase in the nation's population of 3 per cent purely attributable to over-stayers from the UK.

Or could the number-crunchers in Britain, who assert that their figures are "produced to high professional standards," be wide of the statistical mark?

The Travel Trends statistics derive from the International Passenger Survey, an ONS operation with a team of 240 interviewers. They work every day except 24-26 December, traditionally quiet days for travel.

One in 500 British travellers turning up at UK airports, seaports and tunnel terminals is invited to answer questions about how much they spent abroad, what they have been doing – and, crucially, where they went. But life for the interviewers, and the people who interpret their raw data, is tricky. For instance: the main routes for visitors returning from New Zealand are via Los Angeles, Hong Kong and Singapore. The last of these carries the most passengers, with seven wide-bodied jets a day bringing travellers to Heathrow Terminal 3. Four of these planes arrive in the early hours before 6am – the time the researchers start work.

Only three flights arrive from Singapore later in the day. But survey manager, Roger Smith, says this is taken into account: "We receive information from the CAA about flights that arrive when we are not on duty, and build that into the processing."

Why the dramatic disagreement between UK statisticians and their Kiwi counterparts? New Zealand is the most distant country; maybe travellers' propensity to co-operate with researchers is inversely proportional to the length of the flight, with arrivals more likely to be among the one in six travellers who decline to take part.

Or they may be on the phone to loved ones: the surveyors say: "Many passengers arriving want to use their mobile phones once they land. It is IPS policy not to intrude or interrupt."

Mr Smith stands by his methodology: "We view it as a very robust survey with a very balanced design."

ppp Five countries fared even more dismally than New Zealand in losing British visitors, according to the ONS. In Europe, plucky Iceland, Estonia and Luxembourg plummeted by 34, 47 and 50 per cent respectively.

Mexico, the source of the swine flu epidemic that, you may recall, was going to wipe us all out, dropped 41 per cent. Worst of all: Barbados lost almost 100,000 UK visitors in the course of a year, a fall of 60 per cent to just 86,000.

A shocking collapse. Yet Virgin Atlantic reports that demand has been maintained on flights from Gatwick and Manchester to Barbados despite the recession, while BA has actually boosted flights to the island from nine to 10 a week.

Travel by numbers

Does getting visitor figures right actually matter? Absolutely. The 30 per cent fall in UK travellers to New Zealand cited by the Office for National Statistics (ONS) could lead to a cull in British consular care, cuts in capacity by airlines and car-rental firms, and delays in updating Kiwi guidebooks because of the shrinking market. Travellers may conclude the country on the far side of the world has lost its appeal.

The ONS survey could even turn out to be a self-fulfilling prophecy. It reveals New Zealand lost an average of 1,000 British visitors per week. At that rate, the very last Brit will arrive back on 1 April 2012. That is, of course, a Fool's conclusion. But the Kiwis' claim to more than twice as many British tourists as the UK authorities will concede suggests some official foolishness.

The disparity goes way beyond the margins of statistical error; they cannot both be right. We need a survey to ascertain if anyone has squandered time and money on worthless travel data.