However, continued uncertainty about the eventual status of EU citizens as the Brexit negotiations stumble onwards is prompting many of them to consider whether they have a future here and making others think twice about coming here.
The skills shortage is not simply a problem that can be solved by recruiting from overseas, though. A combination of near-full employment, an ageing population and rapid technological change is compounding the difficulties businesses face in finding people with the right skills.
Already, according to Open University research carried out in July 2017, the shortages are costing UK businesses more than £2 billion a year in higher salaries, recruitment and temporary staffing costs.
The new Government Apprenticeship levy from those companies with an annual pay bill above £3 million only came into force in April this year. Those businesses below the threshold for the levy were also promised financial help towards training apprentices, 100% for 16-18 year-olds and 90% for those aged 19-plus.
The new scheme aims to produce three million new apprentices by 2020. Even if this figure was met, it would still be some years before these newly-qualified young people build up the experience needed to fulfil many roles in the workforce.
More than half of those businesses asked in the OU survey said they were employing people with a lower level of skills than they had been recruiting for and were paying for training to build up those new employees’ skills.
But addressing the skills shortage requires more innovative thinking.
How many businesses have older, long-standing workers who may not be up to date on the latest developments in their fields and are assumed by their employers to be coasting gently into retirement?
As retirement ages are pushed further and further back no business can afford to ignore the potential there may be in these older employees.
Recently, the BBC introduced a scheme called reverse mentoring in which young employees in their 20s were asked to help older colleagues, in this particular case to understand the likes and dislikes of millennials.
However, the idea of reverse mentoring has been spreading into other sectors. It has been used to help bring older employees up to speed with new IT developments and to modernise out-dated working practices.
The corporate mind-set has regarded the over 55s as old and not to be considered for investment or further career progression. But such people could be seen as a resource already being paid for, experienced and committed and worth the investment of time and energy in helping to update their skills to be able to contribute even more productively to the business.