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Migration experts say the UK cannot end freedom of movement from the EU on Brexit day because it has no system to work out who is legally in the country.
The Home Office said on 19 August thatEU freedom of movement would end immediatelyin a no-deal Brexit.
But Oxford University's Migration Observatory said employers will have no way to tell whether EU nationals have arrived after 31 October.
It comes as official figures show EU immigration at its lowest since 2013.
Under the existing system, EU nationals do not have to register their presence in the UK so the Home Office does not have records of when they arrived.
Responding to the announcement that EU immigration to the UK has fallen to its lowest level since 2013, Federation of Small Businesses (FSB) National Chairman Mike Cherry, said: “European business owners and employees are central to the UK’s economic success.
"One in five small employers rely on the skills of EU citizens and - with employment levels at record-highs - one in three now say finding the right staff is a major barrier to growth.
“A sudden end to free movement on 1 November will make a bad situation worse. Business owners need time to prepare for such a radical change, particularly as 95% of small employers have no experience of using the points-based element of our immigration system."
Gerwyn Davies, senior labour market adviser at the human resources body the Chartered Institute of Personnel and Development has been looking at the latest immigration figures.
“It is no surprise that EU citizens are less keen on coming to the UK to work," he says.
"However, it is curious that fewer EU nationals are leaving the UK for work given the fall in the value of the pound and the continued political uncertainty. It seems possible that many EU citizens who have yet to secure settled status may be fearful of the consequences of leaving the UK if they wish to return, especially those EU citizens who have yet to secure settled status.
"The prospect of migration restrictions may therefore perversely be helping employers to ease their recruitment difficulties in the short-term."
Matthew Fell, chief UK policy director at the CBI, says that the decline in net immigration in the UK as well as record low employment "means that skills shortages are getting worse".
“Business understands that free movement is ending, but it marks a huge change in the way firms access skills and labour. They’ll need proper time to adapt to a new system.
“The announcement that free movement will end immediately in a ‘no deal’ has left employers and their employees asking fundamental questions about what this means for them. They urgently need this clarified.”
UK net immigration numbers have fallen to their lowest level in six years, according to new data from the Office for National Statistics.
During the 12 months to the end of March, some 612,000 people moved to the UK while 385,000 people emigrated. This reduced net immigration to 226,000, its lowest since the 12 months to the end of December 2013.
Meanwhile, the ONS admitted on Wednesday that the level of migration from the EU to the UK had been underestimated from the mid-2000s to 2016.