The retailer has launched new ranges of pork and lamb in stores from this week and a new-look Finest beef range is to be unveiled in the summer.
Tesco commercial director Steve Murrells said: "We are seeing very strong growth in Finest of 50+% year-on-year, so it is absolutely right to widen the range of Finest meat products we offer.
"It has taken us some time to develop a range that we think meets the grade on consistent quality, but we are confident that with the focus on traditional butchery and maximum tenderness, we've got there.
"Customers tell us they are increasingly concerned with provenance and quality and we hope this range will re-kindle their interest in buying top quality British meat."
All three ranges will consist of meat that has been matured for optimum levels of tenderness and sourced from a select group of farmers.
Finest pork is being reared from younger outdoor-bred pigs, selected from East Anglian farms. The Finest lamb range comes from animals fed on a grass-based diet for a unique flavour. It will be British when in season and New Zealand at other times.
In preparing the meat, Tesco is using traditional butchery techniques to offer cuts such as rib eye pork, which is designed to bring out the best attributes of the animal.
Packaging features simpler cooking instructions to help customers prepare the meat.