Correct English: "You Are Back in London"

The grammatically correct sentence is:

"You are back in London."

Why

• "Back in London" = prepositional phrase meaning "in London again after being away." Requires a verb (are) to form a complete sentence.
• "You to London" lacks a main verb. "To London" is an infinitive/prepositional fragment; it cannot stand alone as a predicate.

Correct Alternatives for "You to London"

• "You are going to London." (present continuous)
• "You went to London." (past)
• "You will go to London." (future)
• "You have been to London." (present perfect)

Use "You are back in London" when someone has returned after a trip. Use a full verb phrase for travel plans or past trips.