Why Britain's battleships disappeared after the war

Would Britain have retained its wartime battleships if carriers had not become dominant?

Possibly, especially if another power built battleships, but without that threat the costly refits were hard to justify and carriers took priority.

Carrier ascendancy mattered, but the calculation also depended on the threat. The surviving British battleships needed serious and expensive refits after wartime service. A substantial Soviet battleship program could have justified keeping and modernizing the King George V class and Vanguard. Without an opponent building comparable ships, scarce money went to carriers and other capabilities with clearer Cold War uses.