What about a K-design battlecruiser as a base for a fast battleship?
Short answerIt is a plausible starting point in the Tillman III scenario, though Britain would also need to invest in supporting infrastructure.
NotesA K-design battlecruiser is a plausible starting point for Britain's response in the Tillman III scenario. Developing it into a fast battleship would also require investment in supporting infrastructure. Other design routes remain possible, so the proposal is a preferred option rather than an inevitable British choice.