How NATO planned to counter Sverdlov cruisers

How did NATO plan to counter Sverdlov cruisers, and how did British and American approaches change over time?

Britain relied on destroyer torpedoes, Vanguard, and light cruisers before Buccaneer became a strong strike capability in the mid-1960s.

Britain pursued Buccaneer to provide a strike capability against ships such as Sverdlov. Work began around 1952, while a strong operational capability arrived only around the mid-1960s in this assessment. That left a lengthy interim period. Daring-class and other destroyers could use torpedoes against larger opponents, while Vanguard and surviving light cruisers also remained available. The familiar destroyer torpedo attack was a general approach to larger ships, rather than a plan unique to Sverdlov. Although the question requests British and American comparisons, this answer develops the Royal Navy's options.