Tesco has said it will reduce the price of groceries which have been previously controlled by the Groceries Order.
The legislation was recently scrapped by the Government following concerns that it had been keeping prices artificially high.
However, recent inflation figures showed prices had not fallen despite the removal of the order.
Tesco has written to consumers saying it will introduce long-term promotions.
The supermarket chain has not, however, disclosed how much it will reduce prices by.