It seems to be an iron law of bureaucracies that officials answer the question they decide to hear, not the question you asked. Those of us who thought we had been told how many immigrants are working here have discovered, this week, that we had been told something else entirely.

When Peter Hain said that there were 800,000 foreign workers in Britain, he had apparently meant — oops! — 1.1 million. And those, it turned out, were only people who had got jobs that had been created since 1997. Except — oops! — that the National Statistician had already told us in July that there were 1.5 million of them. And hers was also an underestimate — oops! — because the Labour Force Survey on which it is based does not include anyone who is foreign-born but has now become a UK citizen, anyone who expects to work here for less than a year, anyone who has lived at their current address for less than six months and anyone who was getting a few beers in at the Walkabout pub when the Labour Force Survey rang their doorbell. Oops!

Knocking on doors may have been fine for the compilers of the Domesday Book, when the population was less than four million, there wasn't much to do of an evening, and the compilers were armed with swords. As a way of tracking the unprecedented movement of people around the globe today, it is facile. I now understand why ministers have never tried to estimate illegals: they can't even count those who are paying tax; let alone dependants, who local councils claim are using doctors and schools for which they have insufficient government grant.

It is diabolically difficult to count people in a dynamic economy. But this whole saga betrays a limpness of purpose and a reluctance to acknowledge, let alone debate, what has been a deliberate policy of mass immigration.

Does it matter if ministers make mistakes? The difference between 800,000 and 1.1 million is tiny: about 1 per cent of the labour force. But it does matter that vague estimates are presented as hard data. And that they always seem to be underestimates, never errors in the other direction. The official habit of underplaying population shifts has had the effect of censoring debate. Anyone who expresses concern can be accused of exaggerating.

There has also been a tendency to talk as if the immigration question is almost exclusively Eastern European. On Monday, according to the BBC, Liam Byrne, the Immigration Minister, called Tory proposals for annual limits a “smokescreen”, because 80 per cent of immigrants to Britain are Eastern European and are entitled to come here. But if that was true, Mr Bryne's proposals for a points system would be unworkable by the same token. In fact, government figures suggest that only about a third of migrants are from the accession countries.

With the notable exception of Mr Byrne himself, ministers still tend to treat the subject as if it were entirely a question of economics. Of course immigrants make a positive contribution to the economy. One of the peculiarities of the Prime Minister's slogan of “British jobs for British workers” is that some of our jobs only exist as a direct result of the skills and spending power of the immigrants, who are boosting the economy. But the equation is complex: higher economic growth translates into better living standards for the elite, who enjoy cheaper builders and cleaners, but not necessarily for builders whose wages have been undercut.

But we cannot simply reduce people to statistics. We are human beings, not units of production. In a densely populated country there are deep human concerns about strangers that have nothing to do with race but everything to do with the pace of change. The Office for National Statistics (which you are also at liberty not to believe) predicts that the UK population will grow from 60 million to 70 million in 20 years, mostly owing to migration and migrant births. That would be a change unprecedented in our history.

So this issue really is all about numbers. But not perhaps in the way the Government thinks. It is setting up a committee of economists, which will help to establish a new points system by deciding how many workers the economy needs. But the idea that you could predict those needs is it in itself wildly old-fashioned.

There is only one part of the economy where you can reliably predict how many workers you will need. That is medicine. And there a row is going on that shows the confusion at the heart of government. Ten years ago a decision was taken to expand medical schools, with the explicit intention of making the UK less reliant on foreign doctors. More British graduates came through the system, costing the NHS £250,000 apiece. But some are ending up unemployed. The Department of Health (DH) says that at least 1,200 of those graduates will be unable to get a job this year, because of competition from non-EU applicants.

Medicine is not a normal market: the training and posts are funded by the taxpayer. The DH wants to give priority to good UK applicants. But the Home Office will not alter its Highly Skilled Migrants Programme.

This little twist to the summer saga of junior doctors was only brought to light, in the British Medical Journal, by a retired doctor, Graham Winyard. Immigration is still too sensitive for other medics to discuss.

The question is no longer whether immigrants are good or bad. They are generally good. It is how many the country can cope with in one go. That is why we have to get the numbers right. The only way to do that is to re-establish embarkation controls and laboriously count who comes in and out. Some people in government feel that would be too expensive. But the political cost of having lost control is mounting by the day.

Times Recommends

• Fantasy world fuelled by sex, drink and drugs
• In short, the story is growing on us again
• A literary feast that I can’t wolf down