Factual error: Foyle is subordinate to an Assistant Commissioner of the Metropolitan Police, but Hastings had its own force (merged with other Sussex forces 1943-47) and the Met had no jurisdiction outside London.
Factual error: Sergeant Brooks calls Det Sgt Milner "Sir" but they are of equal rank.
Factual error: Foyle is a Chief Superintendent. But the series is set during the Second World War and the rank was not introduced until 1949.
Answer: He doesn't actually wear it all the time even in summer. In some episodes in the summer he simply wears his suit with jacket.