By Dominic Casciani
BBC News community affairs
No past estimates of illegal immigrants have been published
Put the words "illegal" and "immigrant" next to each other in the same sentence and you've usually got a political row in the making.
During the 2005 general election, a good deal of hot air was expelled trying to work out how many unauthorised migrants were living within our shores.
More recently, the new Home Secretary John Reid came under fire after one of his top officials, David Roberts, plainly told MPs on Tuesday there was little point hunting individuals who overstay their visa.
But the new immigration minister, Liam Byrne, has now opened up the debate in a way never seen before by saying it's "too early" to rule out an amnesty for illegal migrants aka people working in the black economy.
The question now is whether an amnesty will happen - and if so what would be the implications?
Shortly after the 2005 general election campaign, the Home Office published "best guess" figures on illegal immigration drawn up by experts in the field.
The figures ranged from 310,000 to 570,000, depending on how you approached the mathematics and how much latitude you built in for under-estimates or exaggeration.
Deporting illegal immigrants can prove problematic
However, the higher figure is remarkably close to the numbers of immigration over-stayers and unauthorised workers who have been counted by amnesties in Spain and Italy, suggesting that perhaps there is some truth in the maths.
But, turning to the UK, what do we understand 570,000 illegal immigrants to mean?
To critics of the UK's immigration policies it equates to the population of Edinburgh, a stark image of a public burden if they were all in one place.
On the other hand, were 570,000 people spread evenly, they would represent just less than one per cent of the British population.
In reality, experience shows migrants of all sorts generally cluster in fairly noticeable ways, including where members of their community already live and where jobs are readily available.
While this has been complicated by the government's policy of dispersing asylum seekers to cheap housing around the country, the real day-to-day problems of identifying "illegals" lie behind the Home Office's recent plain-talking.
Let's look at two areas of London: Camberwell in the south and Earls Court in the west.
Anyone local will tell you Camberwell is a hub of west African culture. Earls Court is a well-known stomping ground for Antipodeans.
If you were a Nigerian student looking to earn some cash driving a taxi, as many do, or a New Zealand gap-year kid seeking cash-in-hand bar work, you'd know where to go - especially if your visa had run out and you were not in the mood to go home. In short, these people simply disappear into the largely undeclared economy.
AMNESTIIES: RECENT FIGURES
France: 152,000 (1998)
Greece: 397,000 (1998)
Italy: 308,000 (1998)
Spain: 700,000 (2005)
Source: Individual governments
In the case of other groups, such as the well-documented unauthorised Chinese arrivals into the catering trade, the individuals are likely to live in over-crowded conditions in order to send home as much money as possible - or more often than not, to pay off the people smugglers who got them here in the first place.
Many opponents of migration say the government has failed to work out the burden that more people places on public services, such as interpreters in GP surgeries and English language classes for children.
But in cities that have experienced lots of migration that burden is difficult to calculate - not least if the illegal migrants are working quietly in black-market jobs, with little contact with authorities in areas used to absorbing different communities.
What happens now?
What ministers now do about these people is the great unanswered question and lies behind Liam Byrne's opened up of a debate.
Ministers essentially have three options: they can choose to ignore over-stayers and illegal immigrants, try to find and deport them, or "regularise" their position by offering an amnesty.
Working on the basis most illegal entrants are in the black economy, ignoring them is naturally the easiest thing to do. Indeed, some economists say ignoring illegals benefits industrialised nations by keeping deflationary pressure on wages and prices.
That approach however does nothing to prevent future illegal immigration or do anything to attack the international criminal networks often associated with the smuggling of workers across borders.
Deporting has proved problematic, as the recent foreign criminals furore has shown. It's also extremely expensive, costing up to £11,000 to deport one individual.
Which leaves the politically controversial idea of an amnesty.
These are common in some Mediterranean countries - Italy has run five and Spain six exercises in the past 20 years.
But America has been politically divided over current proposals to naturalize up to 11m illegal workers.
Supporters of amnesties say they reduce illegal working and the hold of criminal gangs, while also raising taxes.
But the counter argument is they reward illegal immigration and act as a pull factor for more of the same.
The critical factor which changes the nature of the game in the UK is the imminent arrival of the Home Office's much-vaunted e-borders programme.
The system will electronically count all movements in and out of ports.
What this should mean, in practice, is that if someone over-stays their visa, somewhere in the Home Office a computer will beep.
Supporters of an amnesty argue it could work if the deal was offered to illegal immigrants as e-borders came online: bringing people into the system while providing a means of identifying any future over-stayers.
But by definition, the illegal entrants who arrive clandestinely on the back of lorries would remain the hardest to find as will still have avoided contact with the authorities.