The same strain of listeria was identified in meat produced by North Country Cooked Meats, which was used in some of the sandwiches sold by the Good Food Chain, the FSA added.
Investigators are testing North Country’s supply chain and examining historical detections of listeria.
The meat producer voluntarily stopped distributing on June 3 and withdrew all of its ready-to-eat products on a precautionary basis, the FSA said.
Listeria infection is rare and usually causes a mild illness in healthy people.
But it can have more serious consequences among those with pre-existing medical conditions, pregnant women and those with a weak immune system.
The Good Food Chain will have to reapply for accreditation before it can directly supply to the NHS again.
Eight hospitals in seven NHS Trusts have reported cases of listeria linked to pre-packed sandwiches and salads eaten by patients.