Could you tell me if there is any difference between "I've been to London" and "I've been in London". Actually, Is it possible to use the second variant or this form doesn't exist at all.

Yes, there is a difference, in most instances where you want to say you have visited somewhere, you say you have been to that place:

"I've been to London."

"I've been to the cinema."

"I've just been to the toilet."

In these cases you are using been as the other past participle of go, and you have to use to as the preposition.

However, if you are using been as the past participle, and want to indicate a state, or for how long you were somewhere, you can use been in.

All the best,

Well really not much one is more proper then the other