During the 1935 design process for the KGVs a number of main armament options were examined based on the old WNT Treaty limit of 16" guns.
1. 3x4 gun 14"
2. 3x3 gun 15"
3. 3x3 gun 16"
The design of all 3 weapons had much in common allowing a scaling from one size to another in manufacture.
The design for the KGVs originally selected in 1935 was the 15" version. BUT that choice only lasted for a few weeks. A political decision was then made to go to the London Conference, which started in Dec 1935, to argue for a new, reduced, 14" limit. That became the new limit in the 1936 Treaty but with the "Escalator Clause". The hope was if everyone adopted the new limit, particularly the USA, the cost of new ships would be reduced.
The 15" design never progressed beyond an outline design and is generally forgotten about.
Also forgotten is that the USN initially designed the North Carolinas around quad 14" before deciding to go to the max size permitted by Treaty - 16", following Japan failing to indicate agreement, as a non signatory, to adhere to the new limit, so triggering the escalator clause. Unfortunately that came too late for Britain & the KGV design.
See Friedman's British Battleships book.
British ship designers felt they couldn't get a "balanced" (in terms of armament, armour & speed mix) 16" armed battleship on the Treaty limit of 35,000 tons. So the 15" option was considered the next best. The decision to reduce the KGV armament from 12 to 10 guns involved discussions about various trade offs involved in meeting the 35,000 ton Treaty limit. At that point they needed to save about 500 tons on the detailed design. IIRC to have carried 12 guns some secondary 5.25" DP armament would have had to be sacrificed or a move to 4.5", neither of which was considered acceptable.
Details of the new 15" gun can be found here.
navweaps.com