Have you ever been to London?
Have you ever gone to London?
Which one is correct?
I think you want to know the difference between "go to some place" and "have been to some place". The difference is that when you use "go to," you are talking about the action of just going to that place. Whereas, when you use "have been to," you're talking about the action of going and coming back. That's the difference between "go to a place" and "have been to a place". In your sentences:
Both of these sentences are correct. There is a slight difference in meaning. In the first one, the speaker is asking about the listener's visit to London (action of returning included). In the second one, the speaker is just asking about the action of going to London (action of returning excluded). I hope that it's clear now. By the way, the first sentence is commoner than the second one.