Why the first postwar warships were still gun-armed

Were the major navies' first postwar warships still armed with guns rather than missiles?

Yes. The 1950s generation, including the Daring class, remained gun-armed; shipboard missiles became prominent in the 1960s.

The first postwar generation belongs firmly in the 1950s, before missiles became the normal basis of a surface combatant's armament. The Daring-class destroyers are a representative British example. These newly constructed ships were designed around guns because that was the mature weapon system available. The missile transition belongs mainly to the following decade, so period labels should not be mistaken for an immediate technology break.