In the movie Greyhound is a Fletcher class destroyer. The crossing took place in February 1942. The first Fletchers were completed only in March and commissioned in June 1942. In the book, Greyhound was a Mahan class destroyer. This class was built in the mid 30s. Still, the Fletchers were the quintessential American destroyer of WW2. Fine ships.
Later in the war the RN formed hunter killer groups dedicated to hunting u-boats.