I'd stake my reputation on this being one of the LEANDER CLASS or "PERTH CLASS" (modified Leanders). Not just because of the main gun turrets, but just the general layout of the upper works and funnels.
The best site I've found for this class is: perthone.com
It has lots of info and nice line drawings ... port side and overview.
To name a specific ship in this class, I''d pick HMAS PERTH only because of her battle history.
(The last book I read about the fighting in and around Sunda Strait just plain made me cry ... the book was about the USS HOUSTON and how she went into her last action with one turret out of action and the barrels on her other 6 8-inch rifles nearly shot out ... to the point where the barrel liners themselves were protruding out the the front of the gun tubes!!! Also the insanely low number of 8" projectiles she still had available for the 6 working rifles for her final fight with the IJN. I forget the number ... but it was the equivalent of bringing a stick to a gunfight.
I always choke up when I read those kind of stories ... the Light Brigade ... VT-8 at Midway ... even Custer (less Custer himself than the poor *******s that went into battle with him). In the face of certain death ... suck it up and do your job like everything in the world depends on it ... and to hell with what comes next.