How well would British battlecruisers fare in a sustained gun action?
Short answerThey could fight the Kongo class and similar ships, but confined waters such as the Mediterranean would deny them the speed and maneuver that made the design work.
NotesA battlecruiser's protection depends partly on having enough sea room to control the engagement. Renown, Repulse, and Hood could use speed and maneuver to choose range against another battlecruiser, and a gun duel with the Kongo class or anything lighter was acceptable. Concentrating them in the Mediterranean against the Italian fleet removes much of that freedom because geography limits the direction and distance of withdrawal. Once forced to remain under heavy gunfire, their design tradeoff becomes much less favorable. The exchange shows why a ship's tactical value changes with theater geometry rather than following from armor and guns alone.