They're both correct, but the connotation is different in each. Do you have friends in London? = I'm expecting that you most likely do have friends in London. Do you have any friends in London? = You might not actually have friends in London. I'm not expecting that you will, but you might, and if you do, they're probably not a lot and might be unusual friendships. For example, you can ask someone who has traveled to London quite a lot, "Do you have friends in London?" And you can ask someone who you know knows people from all over the world, "Do you have any friends in London?" Also, think of it this way: if someone smokes you would go to their house and ask "do you have a cigarette?" Whereas if you went to a nonsmoker's house who just recently quit and might still have a pack lying around you'd ask, "do you have any cigarettes?"

Hi! The second one is more grammatically correct because we use "any" with plural nouns, because if it was singular we would say "do you have a friend in london" not "do you have friend in London"

'any' opens the question to all types of answer. Without it the question could be asking for a limited type of friend.