How do you say this in English (UK)? Have you read the book I gave you last week / had you read the book I gave you last week? Which one is correct?

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Both are correct but the meanings are different.

Have you read the book I gave you last week? Ты прочитал книгу, которую я дал тебе (вероятно, после того, как я дал ее тебе)? "Have you...?" is a question about the present - about how things are now. I gave you a book. Have you now read it? Я дал тебе книгу. Теперь ты прочитал эту книгу?

Had you read the book I gave you last week? Ты уже прочитал книгу до того, как я дал ее тебе? "Had you...?" is a question about the past, about a time suggested by the context. In this case, the context suggests the time when the book was given.