Background information on undocumented migrants
Undocumented Migrants are those who do not fall into any of the UK's legal categories. Three groups account for most undocumented migrants:
(a) those who entered the country without valid documents, including people crossing the Irish border into Northern Ireland clandestinely and those arriving over the water, including the English Channel
(b) those who entered with valid visas but overstayed their visas' expiration or otherwise violated the terms of their admission Illegal Working.
(c) those who have had their asylum and refugee request rejected, cancelled or revoked Unsuccessful Applications.
Some undocumented migrants are asylum applicants who have not yet begun the asylum process from which they would then become asylum-seekers.
Undocumented migrants have previously and are continuously also referred to as unauthorized migrants, illegal immigrants, illegal aliens, and undocumented aliens.
The definition of the term illegals is far from clear: does it refer to asylum seekers whose claims are turned down, immigrants who enter the country illegally, those who overstay their visa, or perhaps those who work illegally while claiming asylum? The press often refers to illegal immigrants or illegals but is often unclear about why the demographic that they are discussing is illegal.
The term Illegal asylum seeker is invalid because as the UK is a signatory to the 1951 UN Convention on Refugees, under international law nationals of other countries arriving in the UK have the right to apply for asylum against persecution and have their request considered. An asylum seeker is someone who has applied for asylum, and is waiting for a decision (whatever the merits of their case). Therefore there can be no such thing as an illegal asylum seeker because it cannot be illegal to seek asylum in the UK.
Undocumented migrant numbers are never accurate for obvious reasons, but numbers can be estimated by subtracting legal foreign-born residents in the UK who are documented from the total foreign-born population that there are records for.