Yes, animal names are used as terms of endearment in British English definitely, but not the ones you find in German, and not as often. Calling someone a "worm" in English is an insult, for example, and "mouse" implies exaggerated shyness.
Off the top of my head, the following are used across the country, but they differ quite substantially depending on region:
#18: "Greedy little pig" is the closest I can come up with, but I'm not sure how that's supposed to be endearing. Maybe something with "bear"?
ETA: Don't be surprised to be referred to as "my lover" by complete strangers if you're ever visiting the west of England, by the way. It's used by men and women to both men and women, regardless of sex, and not to be understood as an expression of romantic love.