hello and some help please

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Hi my name trevor,
am try to identify the cap badge of my grandads brother from the first world war. Its for my grandsons school project but also for my own interest. have attached a picture hope its come out all right!. He was in the 3rd 10th london regiment. date on the paperwork is 14th may 1915 for his medical ? but other paperwork shows 1st Northampton Regt 24-4-1919 on his discharge documents. some other documents show he was in Egypt and Solonica and back to Egypt.
any help would be great
thanks