Conservative Party leadership candidates are being urged to lower the salary limit for migrant labour post-Brexit from £30,000 to £20,000.
The Immigration White Paper, published in December last year, includes plans to scrap the cap for skilled workers and a minimum salary requirement of £30,000 for skilled migrants seeking five-year visas.
But a consortium of businesses and public bodies are spearheading the #FullStrength campaign, which aims to put pressure on Boris Johnson and Jeremy Hunt to ensure there is no skill shortages once the UK leaves the EU.
The group, which consists of the likes of the British Retail Consortium, also call for an extension on the temporary work route for migrant workers from one year to two.
Farming organisations have also frequently warned that rural businesses post-Brexit may find it hard to find labour if rules are too restrictive.
The National Sheep Association (NSA) has urged the government to reconsider the UK's future migration policy to ensure wider agriculture is not damaged.
It says that on average UK abattoirs are more than 75% reliant on migrant labour, and that foreign veterinary cover is often even higher than this.
As well as abattoir vets, whose salaries often do not reach the £30k cut off, the sheep sector is also concerned that not enough consideration is being given to general staffing needs in abattoirs.
The joint letter by the #FullStrength campaign says: “Our country needs a fair and managed immigration system that keeps it open to all levels of talent that our economy and local services sorely need.
“It is crucial that this system recognises the benefits of international talent whilst ensuring the right controls are in place for managing immigration more effectively, necessary for ensuring the public’s trust.
“Without the ability to access international talent, many of our world-class sectors are at significant risk.”
It adds: “As the UK prepares to leave the EU in the near future, it is imperative that the government puts in place measures that will avoid employers facing a cliff-edge in recruitment, and works towards building a successful economy that is open and attractive.”
On immigration, Mr Johnson favours an Australian-style points-based immigration system while Mr Hunt wants to review the £30,000 salary minimum.