Its latest Convenience Tracking survey says 16% of shoppers bought bread in c-stores in 2002 compared to 10% in 2001, and 17% bought milk compared to 16%.
HIM md Tom Fender said: "It's good to see that basket penetrations are on the increase. This points to the fact that retailers are at last tackling the problems of non-availability and turning away from the misguided culture of it's been a good day as we sold out by 4pm' which has existed for far too long."
HIM data suggests chilled basket penetration has increased from 9% in 2001 to 13% this year, with buyers spending an average of Â£5.58, Â£1.66 more than the average c-store shopper.
A high proportion of the shoppers were found to be regulars, with 54% saying they normally bought chilled items from their local store. The biggest cross purchases were milk and bread.
The majority of chilled customers, 65%, were price ignorant.