to this day in 1974 when, on a visit to the South Pacific, Princess Anne wore a light picture hat. Likely a design of John Boyd, the hat looks to be made of textured straw (or roughly pleated voile?) casually wrapped in a folded silk scarf as a hatband that trails down the back. Effortless and chic.
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Photo from Getty as indicated
Royal Hats 
This does seem to go with Anne’s effortless and practical style. It also looks very cool in what looks to be a hot and sunny climate.
Appropriate timing for a John Boyd hat, and a perfect hat for the occasion. Also seems like a good choice for the very practical Princess Anne, as it looks like it could easily be altered to go with other outfits by simply replacing the scarf. Agree with SoCalGal that I wish there were a color photo!
The Princess Royal looks cool and chic but I dearly wish we had a color photograph. I’m dying to see the colors in the silk scarf; the pattern looks very “groovy” and right in keeping with the times.
Most attractive.