In the US there is a slight difference in meaning. “Have” for something closer and better in a question”, “take” for something further away and better for the imperative.
People are crowded around a photograph and I can’t see it. “Hey guys, can I have a look?”
Today’s crossword is a killer. Here, have a look and see if you can get any I’m stuck on. (Gives the other person the puzzle) (“take” would be fine too but I would slightly prefer have)
I heard you got a new car. Can I see it? It’s in the garage. Go take a look. (“Have a look” in this situation would sound British to me)