The Royal Navy could have developed the 5.5-inch gun further

Did the Royal Navy miss an opportunity by not developing the 5.5-inch gun as a lighter alternative to the 6-inch weapon?

Yes; the 5.5-inch gun was a promising system that could have offered much of a 6-inch gun's effect at lower weight.

The attraction is a useful balance between shell effect and mounting weight rather than maximum caliber alone. A 5.5-inch weapon promised much of the striking effect associated with a 6-inch cruiser gun while imposing a smaller burden on the ship. That trade could support more barrels, lighter mountings, or weight reserved for armor and machinery. Further development would therefore have given British designers more freedom in armament layout, protection, and displacement on cruiser-sized hulls.