Around 2,500 jobs at Palmer and Harvey will be lost straight away. The firm has depots at Cross Green and Gelderd Road, and runs an apprenticeship scheme.
Talks failed to save the struggling business, which was in debt to several suppliers.
It supplies goods such as tobacco, alcohol and sweets to 90,000 convenience stores, newsagents and petrol stations across the country.
The company has a total of 3,400 staff.