Given that he died in September 1918* and the record specifically says "1 1/4th miles south of Peronne" leads to the conclusion that he perished fighting in the Second Battle of the Somme, one of the most important stages of the infamous Hundred Days Offensive. I can only assume your granduncle was Australian or Canadian, as they did the bulk of the fighting near Peronne and then later St. Quentin as the offensive drove deeper.

Now this is where I draw some confusion on how he died. As you can see from this map (and just looking at battle records), the area just south of Peronne was breached during the period between the 30th of August and the 4th of September by Australian forces. There are no other battles which were nearby Peronne unless you go quite a few miles Eastward to St. Quentin or Northeastward to Cambrai, where the Canadians fought. So I'd ascertain that your granduncle, if Australian, fought in the Second Battle of the Somme during the Australian Corps breakthrough, was injured, and died a week or two later out of complications on his injury. Otherwise he had to have been stationed as a support unit and died of disease or some other factor as the area in and around Peronne was secure 2 weeks before your granduncle perished. That or he fought in St. Quentin, was injured, and died in the reserve camp which I would assume would be stationed in/around Peronne.

It would depend on a number of factors. I would recommend that you start here, which is our guide on searching for military records, and might be helpful for you.