The practice of reusing the names of ships lost in WWII was a largely unique US Navy practice. After their losses, the names of Yorktown, Hornet, Wasp, and Lexington were all used for Essex-class carriers. But it wasn't confined to just carriers. Other ships reside names.

When the the heavy cruiser USS Houston (CA-7) was lost to Japanese torpedoes in March 1942, it was soon replaced by the USS Houston (CL-81).

Why? Morale-boosting. A savvy US Navy recruiting officer, Clarence Taylor, hit upon a scheme. With the cry of "avenge Houston!" Taylor rallied Houstonians to replace the nearly one thousand men lost on the USS Houston. The public response was overwhelming. Nearly 1,400 men jammed into downtown Houston for a mass swearing-in ceremony conducted by Rear Admiral William Glassford. One 16 year old who had lost his brother in the Houston was even allowed to take part, despite the fact he was legally too young (his official oath was taken three days later, by the same officer who had inducted his brother).

In response to the groundswell of popular response, a Cleveland-class light cruiser under construction was renamed the USS Houston (CL-81). FDR declared: "Our enemies have given us the chance to prove that there will be another USS Houston, and yet another USS Houston if that becomes necessary, and still another USS Houston as long as American ideals are in jeopardy."

The British did reuse some names shortly after the war. The lost carrier Ark Royal was replaced by another carrier of the same name in 1950. But none during the war, as far as I know.

http://www.thc.texas.gov/preserve/projects-and-programs/military-history/texas-world-war-ii/houston-volunteers Ship of Ghosts by James D. Hornfischer