Fold back the leather and look just under the edge of the lining. Herbert Johnson used to attach a slip to the lining which told the year of manufacture. I do not know if they did this for hats re-branded for Brooks, but it was true of all of their London hats...at least up to 1982. Something happened to H.J. in the early eighties and the hats they started to produce...and still produce...were and are relative crap. I would say that any H.J. produced prior to 1982 could be a good investment if it has received good care through the decades. I would avoid any post-1982 H.J., lousy felt and poor quality manufacturing and finishing. At least in my experience.
By the way, I believe that the hat pictured is a Herbert Johnson "Grosvenor," which is the hat I always wore from the early seventies until I started having my hats custom made by Gary White. Gary still copies an old Grosvenor of mine for my hats.
Buzz