At the time this projectile was manufactured there were potentially 4 marks of 4.5" gun in service across the Fleet. Mks I, III, IV & V, the Mk II was Land Service AA and was declared obsolete at the end of WWII. The 4.5" started life as QF fixed (Mks I & II) and became QF separate (Mks IV & V) when it was realised that a complete round was too heavy and long for manual handling, there’s conflicting information as to the nature of the Mk III. It’s said that the guns could use either fixed or separate ammunition, which may be true of new guns but is problematical with old guns. A classic example of this is 4" QF where the separate case is about 20mm shorter than the fixed case, if the gun has had a prolonged diet of separate cases, erosion occurs around the point where the case finishes and a pocket develops. If a longer fixed case is then fired, the mouth of the case is forced into the pocket making extraction very difficult.
Although your projectile has a cannelure, it does not mean that it was intended for QF fixed, as previously stated there was potentially 4 different marks in service and thus a universal projectile body was introduced. This cannelure appears to have survived to almost the end of the Mk V gun which was many years after the QF fixed guns had been declared obsolete.
The base of the projectile is puzzling, unless we adopted the German method of filling HE shells - they used a precast HE pellet inserted from the base, I can’t see a purpose for the larger plug. The smaller plug is a tracer blanking plug. The Army Mk II gun used a projectile fitted with Tracer, Shell, No.1 which is an external tracer about 20mm in diameter extending some 50mm from the base. This isn’t a problem with fixed ammunition, but causes all manner of problems with separate ammunition - such a ramming and the closing cups of the cases have to designed to accommodate the intrusion. That said I don’t know if that was the intended tracer for the separate ammunition and that plug is quite a bit bigger than the tracer.
Again with this period of time and the size of the Fleet, the only reliable way to ascertain without doubt what guns a vessel was fitted with is to make reference to the gun logs. These chart the history of the guns from being taken on charge, to their final disposal. With respect to RAN vessels for this period, I don’t know if those records would have been held by the RN or RAN.