The supermarket chain Waitrose is rebranding the lamb ready meals in its "British" range because some are made with lamb from New Zealand.
The problem emerged last year when it was noticed that the lamb meals in the range did not in fact use British meat.
At first, stickers were put on the front of the packs making it clear where the lamb came from.
Now all the "British" lamb meals will be rebranded as "Classic", though not meals made from pork, beef and chicken.
All the meat included in those products already comes only from the UK.
"To ensure the provenance of the lamb in the meals is clearer (it has always been on back of pack) we have [already] stickered all packs on the front," said a Waitrose spokeswoman.
"We are about to re-launch the range with the branding "Classic", removing the large "British" reference from the front of pack.
"This was only ever supposed to denote the origin of the recipe but we understand why confusion has arisen," she added.
The National Farmers Union (NFU) welcomed the change.
"We made our concerns very clear to Waitrose right from the beginning on this product," said NFU President Meurig Raymond.
"The inclusion of the word "British" in the brand name despite the meat being sourced from New Zealand is misleading for shoppers - and it's frustrating for British farmers, especially those who produce lamb Waitrose could have sourced."
It is not the first time that Waitrose has been criticised over the use of New Zealand lamb.
Last April the National Sheep Association accused the company of misleading some shoppers by selling New Zealand lamb under Waitrose's organic "Duchy" brand name during the winter when organic UK lamb is not available.
Waitrose has now asked it suppliers to try to get more British meat into its ready meals.
"At the moment, because of our policy of buying and using the whole carcass from dedicated suppliers, we do not have sufficient raw material available to make this change but, nevertheless, we are exploring this option," Waitrose said.
Among the ready meals being rebranded are lamb hotpot, shepherd's pie and lamb with mint and redcurrant.