A spokeswoman for the Basildon and Thurrock University Hospitals NHS Foundation said "immediate steps" were being taken to improve paediatric services, after it was heavily criticised by the Care Quality Commission (CQC).
She confirmed the CQC inspection two weeks ago was prompted by the death of a 10-year-old girl and a medication overdose of a baby.
It is understood that the girl was treated at the trust before she was transferred to London where she later died. The baby is expected to make a full recovery.
The trust said it could not provide any details about the child's death and the overdose because the cases are both subject to an internal review.
It said that there are more senior staff and nurses on duty at the Essex hospital, especially out of hours, and spot checks were being conducted.
I want to assure the local community that we are absolutely committed to improving the standards of care which we deliver to children.
"By commissioning a review of our paediatric services we can be sure we are looking at every area to best meet their needs.
"We need to do better to ensure that every child who comes to Basildon Hospital gets good, high quality, safe care. Only by doing this will we address the CQC's concerns."