Bud, the beret serves as the uniform head-dress of the AAC. Harry is a subaltern in the Household Cavalry Regiment attached to the AAC and therefore wears the dress trousers and tropical jacket of his parent Regiment with the AAC beret.
'Tradition', I believe it's called.
"... dress trousers and tropical jacket of his parent Regiment with the AAC beret."
And to complete the list, add Cap badge of HCR.