Without knowing the details of the case, no one can begin to answer your question.
However, had the child received the proper supportive hydration and "nutritional" care including intravenous pH-balanced vitamin C at a high dosage and vitamin D-3 boluses at 1000 IU/lb or 2200 IU/kg per day along with a suitable probiotic powder (or 20 micrograms of vitamin K-2 per kg of body weight) for 10 to 14 days until the child's 25-hydroxy vitamin D level( a blood test) approached 250 nanomole/liter with maintenance at a lower level of supplementation and an added 1 to 2 grams of l-lysine be given per day, then the risk of the child's dying would PROBABLY have been significantly reduced. [Note: If the child has a vitamin A deficiency, then appropriate vitamin A supplementation should be included in the nutritional supplementation. The "ideal level for 25-hydrxy vitamin D in the blood is between 137 -- 250 nanomole/liter (55 -- 100 nanogram/mL). This is the case because the body produces its own polypeptide antivirals, anti-fungals, anti-molds, and anti-bacterials agents tailored to fight the infecting organism at a finite level as long as the body's 25-hydroxy vitamin D blood level does not fall below 125 nanomole per liter (50 nanogram per milliliter).]
Moreover, since some vaccinated children vaccinated with the existing live-virus alphaherpes varicella zoster vaccine, commonly misnamed as varicella zoster virus (VZV), also apparently die from the adverse effects of their chickenpox vaccination, absent the appropriate nutritional support suggested, vaccination does NOT necessarily reduce the risk that a given child may die from "chickenpox" -- because the vaccine is a live-virus vaccine and it most certainly does NOT provide lifetime protection from having chickenpox again or, worse, having the primary infection or inoculation infection recur as shingles.
On balance, based on the overall experience in the USA, implementing a "chickenpox" vaccination program in the UK would be at least as problematic and non-cost-effective as the current 2-dose varicella (Merck's Varivax(R)) vaccination program for children and 1-dose herpes zoster (Merck's Zostavax(R)) vaccination program for older adults to reduce the increased cases of "shingles" are in the USA.
If any reader wants to learn about the problems with a mass vaccination for chickenpox, he or she should read the varicella (chickenpox and shingles) articles in which Gary S. Goldman, who once worked as a contractor for a CDC-sponsored active surveillance project for varicella, is the lead author.
Please note the information provided is just that -- information -- it is NOT medical advice NOR, without confirming the validity of the suggestions, should anyone rely upon this information for being other than my current understanding of the nutritional factors that affect the severity of chickenpox cases in children and adults.