The shortage of workers across the UK has been made worse by Brexit, according to a new report.
But other issues facing employers trying to recruit staff include the pandemic and more people taking early retirement, it was suggested.
A report by Oxford University's Migration Observatory said some employers who used to rely on EU workers are now starting to adjust by turning to automation, or cutting back on production.
Madeleine Sumption, director of the Migration Observatory, said: "While it is clear that ending free movement has made it harder for employers in low-wage industries to recruit staff, changing immigration policy to address shortages brings its own set of challenges.
"Low-wage work visa schemes are notoriously difficult to police and often open workers up to exploitation and abuse. It's also surprisingly difficult to measure shortages and work out how to target immigration policy towards them.
"Immigration policy is a bit of blunt instrument when it comes to labour shortages and there's a real trade-off between responding quickly and being evidence-based.
"If the government wants a system that is evidence-based, it can't be expected to respond at short notice to the latest crisis, whether the problem is airports, lorry drivers, the pork industry or something else."