The photo in the OP was thoroughly discussed on another forum last year. A whistle on a chain attached to a boss was an affectation worn by Light Infantry regiment sergeants starting in the 19th century. Although colloquially known as the Inkerman whistle, they were being worn well before the Battle of Inkerman was fought.
The whistle was worn in different ways by the LI regiments. Some wore it with the boss to the left and the whistle to the right and others vice versa. In some forms of dress it might not have been worn at all. It's a very confusing item of dress about which to make precise declarations.
I'm not 100% sure but I think Rifles NCO's still wear it on their uniform.
Cheers,
Dan.
Sergeant of the DLI showing the wearing of the boss on the right and the whistle to the left.