The move means it will no longer stock New Zealand or Australian fresh lamb.
The Bradford-based company announced at the Great Yorkshire Show that it would also recruit more local food and drink makers, and said its buyers were touring the country meeting potential suppliers.
Morrisons claims that more than two thirds of its food is British, compared to a national average of 52 per cent.
Its meat director, Rob Youngson, said: “Customers tell us that they want more homegrown food.”
The provenance of fresh meat is becoming a marketing battleground for retailers, with the Co-op also recently announcing a 100 per cent British policy.
The National Farmers’ Union welcomed the latest move. Earlier this year it was critical of Morrisons for selling Australian and New Zealand meat under its Market Deals brand
NFU deputy president, Minette Batters, said last night: “We are extremely pleased that Morrisons has shown this level of commitment. It will certainly make it easier for shoppers who want to buy British lamb but have previously been confused by the Market Deals labels.”