Now the parents are probably going to sue the doctor because they think he/she is negligent and didn't do his job saving the child while, in reality, he did the best he can but people never seem to notice that. As h3g3l said, it's not something new, and shit happens.
Also, don't expect for doctors to be believing patients or moreso, patient's parents (specially now in days of webmd, where everyone can look up symptoms and diagnose themselves). They though it was meningitis (in the note it doesn't say if it was or not), but the doctor would've needed to do a spinal tap to diagnose meningitis because it's the only way to diagnose a baby with meningitis. I do feel sad for the baby's death, but come on, don't blame the doctor.
Ok I will say that my background is only in US based medical practice, I looked up some basic information on UK paramedic scope of practice and education requirements.
It seems like according to this article it seems like the child was evaluated on the scene by paramedics, and was never bought to the Emergency Department (ED (US) or A&E(UK)) for evaluation by a board-certified Emergency physician or a board-certified pediatrician for further evaluation. While mid-level practitioners have an important place in the health care environment, and can provide excellent care while under the supervision of a qualified physician, they have not undergone the necessary training to diagnose more complex medical conditions and evaluate high-risk patients independently. This case demonstrates an example where a paramedic clearly did not have a strong understanding of his limitations and incorrectly allowed a patient to refuse transport to definitive care.
Furthermore, considering the age of the child further treatment should have been obtained regardless, younger children usually have atypical presentations of influenza, as well as other disease, and can have severe bacteremia, including meningitis, even if they appear healthy or healthier then expected for the severity of the disease. In addition a two year old child would be unable to clearly indicate their symptoms, and additionally are more likely to suffer from complications due to the flu. Again, this is a diagnosis that could have been made in a fully equipped ED where appropriate laboratory studies could have been obtained, but unfortunately it seems like the child was never provided with that level of care.
As far as malpractice goes, in general I feel like in cases of Emergency Care a willful and wanton standard should be applied, while this is not generally the law in the US, I would feel that this will not fall under that standard, and therefore, personally, believe that the provider should not be sued. That said, I feel a review by the licensing authority in order to determine if his actions were within his scope of practice, and if any of the actions he took were inconsistent with his level of licensing. Since this was in the UK and the EMS personnel were employed by the NHS, I would think they would be personally immunized anyways and it would come out of some fund the system set up, but maybe someone from the UK can clarify that.