If I remember right, the pennant number's flag superior of the Tribals was "L" from time of commission until autumn '39; it then changed to "F", and finally to "G" in '41.
Cossack (L03) served with the 1st Destroyer Flotilla in the Mediterranean Sea. Accordingly, she was in 507C light grey ("Mediterranean Grey"). When called back for service in home waters in September '39, she changed for the grim 507A dark grey ("Home Fleet Grey").
So, in summary, likely the picture was taken before the war
I gave the 507C coat to Afridi ...