In a letter to Defra Secretary of State Andrea Leadsom, the NFU, NFU Cymru, NFU Scotland and National Pig Association say doing so would give shoppers more choice and confidence when buying British food and increase transparency in the supply chain.
The organizations have also expressed their concerns over the loss of food name protection when the UK leaves the European Union.
French government trial used as example
A joint statement issued by the groups pointed to the implementation by the French government of a two-year trial of country of origin labeling for milk in processed products, while other European governments have outlined plans to implement country of origin labeling for processed foods.
The statement said a survey carried out by the NFU in May 2016 found 60% of the UK public often or always looks specifically for British produce when shopping for food.
The farming groups stressed that they want to see the continued use of food name protections in the UK that guarantees authenticity and origin and prevents imitation products from using the name.
They cite Stilton cheese as an example, and say the European Protected Geographical Indication (PGI), Protected Designation of Origin (PDO) and Traditional Speciality Guaranteed (TSG) have been vital in protecting food provenance in the marketplace.