By Brian Wheeler
Political reporter, BBC News
When a senior official told MPs he did not have the "faintest idea" how many illegal immigrants there were in the UK it plunged an already battered Home Office into fresh crisis last May.
Migrant workers are filling labour shortages, ministers say
But anyone trying to find the answer to that question in the small forest of immigration statistics released by the government will search in vain.
What they should be able to do, however, is work out how many legal immigrants have come to the UK - although, even here, the figures are open to debate and interpretation.
Close study of the plethora of figures - which cover slightly different time spans and may overlap - suggests more than 1.4m non-British people were given the right to live and/or work in the UK in the two years since May 2004.
Of that total, 427,000 were people registering to work from the eight former Eastern Bloc countries which joined the EU in 2004, with the majority coming from Poland.
Add to that the number of self-employed people from those countries - and here we have to take a Home Office minister's estimate rather than official figures - then the total from the eight former Eastern Bloc states reaches "about 600,000".
There are no figures for the number of children or spouses accompanying the self-employed, but we do know that the 427,000 registered workers brought with them 36,000 dependants.
That brings the total of people given the right to live and/or work in the UK from the new EU member countries to 636,000 since May 2004.
Over the same period, migration from outside the EU also reached record levels, something largely overlooked in the coverage of the accession states.
Some 318,330 people were granted the right to settle in the UK in 2005 and 2004 from non-EU countries, according to Tuesday's figures.
MIGRATION SINCE 2004
Accession countries: 427,000 (about 600,000 including self-employed)
Non-EU settlement: 318,330
Granted asylum: 123,000
Non-EU work permits: 261,235, plus 87,000 dependants
Source: Home Office
The largest increase was in people coming from Africa, which contributed 54,080 new arrivals in 2005 and 39,430 in 2004.
There were also significant increases in people coming from the Indian sub-continent, which contributed 24,235 in 2004 and 28,990 in 2005, and the Middle East, which contributed 9,395 people in 2005, up from 6,045 in 2004.
Immigration from European countries currently outside the EU, such as Turkey, Bulgaria, Romania and the former Soviet Union, also went up over the two year period, to 20,810 in 2005.
Migration from the Americas stayed relatively static.
While many of the people granted right of settlement may have already been in the UK for at least four years, the figure is symbolically important as it represents a more permanent relationship with the country.
If you then factor in people granted permanent settlement under the asylum system in 2004 and 2005, which adds up to 123,000, the total tops a million, although many of those granted asylum may be included in the permanent settlement figures quoted above.
Leaving the UK
The 1,425,000 figure comes once the 261,235 people from outside the EU who were granted work permits over the two year period - and their 87,000 dependants - are added.
This figure does not include people from the existing EU countries - say Ireland, France, Germany etc - who may have moved to live in the UK over those two years. And by definition it does not include illegal immigrants.
Having said all that this does not mean, of course, that the UK's population will have increased by this amount since May 2004, as there have also been people leaving the UK.
For example, 119,000 British people moved abroad in 2004, according to the latest available figures.
There are no figures given for the numbers of people given the right to work in the UK who have since left.
Given that nearly half the new migrants from Eastern Europe are under 25 - and that many of the jobs they do, such as hotel and catering or agricultural work, are seasonal - there is a good chance many will have returned to their country of origin.
Mark Boleat, chairman of the Association of Labour Providers, which represents food processors and gang masters, said the workers registration scheme was not an accurate way of measuring the impact of accession on the British labour market.
"The figures are precise in that they show the number of people who have registered but they don't really tell us how many workers have come to Britain.
"Still less do they tell us how many are in the country. Many workers are not required to register because they are self-employed or they work for less than a month and the figures simply record the people coming in, not those going out.
"And, in addition, we know that many workers have simply not registered."
In Mr Boleat's view "more than 100,000" workers have come to the UK who have not registered to work, although, he adds, the government should know how many are currently working from their National Insurance contributions.
What is certain is that the government grossly underestimated the number of people who would want to come to the UK in search of work when the eight accession countries joined the EU in 2004.
The government originally backed estimates suggesting up to 13,000 a year, rather than the 214,000 a year who have done so.
Home Office minister Tony McNulty has defended the miscalculation, arguing it had only predicted the number of people who would settle in the UK.
"These are economically productive individuals who are making significant contributions to our economy," he told BBC News 24.
He also argues that the rest of Europe is moving in Britain's direction, with Spain, Italy, Greece and Finland now opening their doors to workers from the existing eight accession states.
But, equally, he appears to be preparing the ground for a U-turn on admitting workers from new accession states Bulgaria and Romania.
He has stressed the decision to open the door to workers from these countries was always going to depend on conditions in the UK Labour market.
His cautious tone is in marked contrast to the statements being made by ministers in 2004, in the run up to the first wave of EU expansion.
The debate two years ago centred on fears migrants would exploit the UK's benefits system, something which has not yet happened to any great extent.
The then Trade Secretary Patricia Hewitt dismissed as "nonsense" suggestions there would be a huge influx of workers from Eastern Europe.
The then immigration minister Beverley Hughes - challenged on the issue in the Commons by Labour's John Denham - admitted the UK's policy would have been different if estimates of migrant numbers had been significantly higher than 13,000 a year.
Some estimates based on wage rates in the new accession countries suggest the influx of workers from Bulgaria and Romania could be as high as 620,000 in the first two years. The government has avoided making predictions this time.
No 'open door'
But the scale of its previous miscalculation has prompted some senior politicians, including Mr Denham, who chairs the influential home affairs select committee, to call for a "breathing space" to absorb existing migrants.
AGE OF REGISTERED WORKERS
Under 18: 0.5%
Source: Accession monitoring report May 2004 - June 2006
Ministers seem to be preparing such a move, with Trade Secretary Alistair Darling insisting at the weekend there would be no "open door" to workers from Bulgaria and Romania.
The government argues that migrants are filling gaps in the UK labour market - doing jobs the local population does not want to do and helping to boost the economy and create jobs.
Tuesday's report says migrants are also providing valuable public services, such as driving buses and nursing.
Ministers also point to the fact that only about 700 new EU migrants are claiming unemployment benefits.
But critics of the government's policy, such as former minister Frank Field, say migration is harming the indigenous population's employment prospects and is unsustainable at its current level.
Bus drivers and newly qualified nurses, for example, are finding it harder to get jobs because employers are bringing in cheap labour from Poland and other countries, he argues.
"It is becoming more difficult for local people to get jobs at a time when the number of jobs is increasing," he told BBC Radio 4's Today programme.
It is no coincidence, he adds, that unemployment has been steadily climbing over the past 18 months and is poised to top the politically sensitive one million mark.
Most economists believe mass migration benefited the UK economy, holding down wage inflation and, by extension, mortgage rates.
Campaign group Business for New Europe argues Britain's growth rate has remained ahead of many other European countries because it has opened its doors to new workers from the East.
"The prospect of further migration from Eastern Europe which triggers economic growth is a cause for celebration not cowardice," it adds.
Even Frank Field admits the evidence migration is harming the British economy and jobs market is largely anecdotal at the moment.
But - as Tony McNulty concedes - there has yet to be a proper analysis of the impact the latest influx of migrants has had on the UK labour market.
And that is something ministers now appear to be determined to carry out before opening the door to a fresh wave of workers.
The Office for National Statistics has also argued that better figures are needed on the number of migrant workers around the UK - something that would help the authorities plan the provision of extra services such as health and education.