An inquest is a formal inquiry by a Coroner to determine how someone died and can involve a jury to decide the cause of death. The purpose of an inquest is to establish who, where, when and how a person died and is an investigation, not a trial or adversarial hearing. There is only an inquest under specific circumstances:
The death is violent or unatural
The cause of death is unknown
There is a legal requirement to investigate e.g. a death in prison, whilst sectioned.