Public Health England (PHE) said a batch of a food supplement was "strongly linked" to the death of one baby and the illness of 14 others.
PHE officials have now identified three further cases of septicaemia in babies being treated in neonatal units in hospitals in England, bringing the total number of cases to 18.
The babies, who became unwell last week, are responding to antibiotics, a PHE spokeswoman said.
One case was confirmed at Peterborough City Hospital in Cambridgeshire and two probable cases have been identified at Southend University Hospital and Basildon University Hospital, both in Essex, she said.
PHE has "strongly linked" the cases with a batch of intravenous liquid called parenteral nutrition made by ITH Pharma.
The manufacturer said that the suspected contamination has been traced to a "sourced single raw material ingredient" , but would not be drawn on details.
Speaking outside the company's north-west London base, ITH Pharma managing director Karen Hamling said: "From investigations carried out so far, it would appear the potential contamination is linked to a single sourced raw material ingredient.
"As a mother, as a pharmacist , as someone who has worked for 30 years in healthcare, inside and outside the NHS, I am deeply saddened that one baby has died and 14 others have fallen ill from septicaemia."
Babies in Scotland are not at risk from the contaminated batch of feed.
NHS National Services Scotland confirmed that while it had procured other products from the supplier of the potentially faulty batch, it had not stocked its baby feed.
A spokesman for NHS National Services Scotland said: "We have checked with the supplier and can confirm that no stock of this product has entered the Scottish supply chain."