Own-label sales in the soft cheese, tomato ketchup and corn flakes categories were "ticking up significantly" as a result of Switch & Save, claimed Tom Hampson, Sainsbury's head of national advertising.
The supermarket would continue to use the tactic in all its stores as own label had "performed really well against branded competitors", he said.
But Kellogg's which dominates the corn flake arena cast doubt on the supermarket's claims of success in its category.
"We think when it comes to cereals that Sainsbury's customers might have already voted with their feet," said Colin Bebbington, Kellogg's head of multiples.
"Switch & Save point-of-sale has been placed on branded products across all categories, including ours, for over a year now. But in that time we have continued to grow in Sainsbury's."
He added that Kellogg's welcomed competition "as it makes us better".
Sainsbury's launched Switch & Save in October 2008, provoking outrage from some suppliers, who described it as a deliberate attempt to damage their business.
The discontent grew last year when store sampling tests were branded heavy-handed by suppliers, who accused the supermarket of hard-selling its own-label lines against the brands.