Beckie is representing the parents of baby Walter German in a medical negligence claim against the hospital trust.
Recording a narrative verdict, coroner Sarah Clarke said Walter died as a result of his brain being starved of oxygen, likely due in part to an umbilical cord obstruction.
The civil claim argues that despite the mother's previous third-degree tear reported in her notes, staff at the hospital did not know about the difficulties with her first delivery three years earlier that should have resulted in discussions about a caesarean section.
The Care Quality Commission previously issued a warning notice to the Trust to make significant improvements following an unannounced inspection of the hospital after it had received concerning information about the safety and quality of maternity services.
The report identified a bullying culture in which staff said that they were told to stop reporting unsafe staffing levels.
Beckie told BBC News that Walter's parents were determined that their baby's legacy will ensure improvements in care are made to better protect mothers and babies at the hospital.
The coroner added to her conclusion that "Walter's mother was not seen by an obstetrician during her pregnancy and this led to her being unable to discuss birth options regarding delivery given her previous third degree tear."
Read BBC online coverage
Following conclusion of an inquest into the death of a nine-day-old baby at the Royal Sussex County Hospital in Brighton, Beckie Drew was interviewed by BBC TV News and online.