Why Britain might answer an American nuclear battlecruiser

Would Britain build a battlecruiser if the United States answered the Kirov class with one, and what might it be called?

Possibly one, presented as a limited expense and probably named Queen Elizabeth or Duke of Edinburgh.

The premise imagines the United States building a nuclear-powered answer to Soviet Kirov-class ships. During the 1970s or 1980s Britain was reducing conventional carrier ambitions and moving toward the smaller Invincible class. A single large surface combatant could be sold politically as a bounded one-off expense rather than the start of a broad capital-ship programme. Prestige, allied competition and nuclear-propulsion experience could therefore make one British battlecruiser conceivable. Its name would probably come from the CVA-01 list, with Queen Elizabeth or Duke of Edinburgh given as likely choices.