US: M to United Kingdom Size 6 1/2
Cross-market women’s hat conversion mapping M specifications into 6 1/2.

Analyzing Hat Size Equivalence Across Markets
US: M: Features a head circumference of 56.5 (22.2 ) measured just above the brow and ears.
United Kingdom Size 6 1/2: Features a head circumference of 53 (20.9 ) measured just above the brow and ears.