Tilly, the gov.uk site is quite useful for explaining what happens after death (fairly simple language). Working in ITU, quite a few of our deaths get referred to the coroner, generally when they have died within 24 hours of admission if they have no defined previous medical condition, there is no obvious cause of death, they have died within 24 hours of surgery (if they haven't found obvious secondaries), or the cause of their death is suspicious/result of an accident. The doctor who fills in the death certificate will often ring the coroner for clarification if there is uncertainty whether he should refer or not.
Given that your relative had been unwell for some time, despite her young age, it is unlikely that it was felt a post mortem was necessary.