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The
sentence is conditional 2 that is it
expresses an unreal present.
If + BE + TO + Verb is used when the action depends on some circumstances. We can say in this case: If by chance he had the "opportunity" to succeed, he would need to move to London. or If "by (any) chance" he succeeded, he would need to move to London. or If he succeeded, he would need to move to London. = The guy does not have to move to London because he has no chance to succeed.
The "If" already infers the meaning "by chance or opportunity" = Hypothetical situation
"Were to " can be used to describe hypothetical situations in the present, future, or past. Your sentences is not in past because it doesn�t have the correct structure in order for it to be past. So, it can be either present, or future, because the structure is correct for both. So, in order to check the tense, you need to revise the meaning of the sentence... When you say "He would need to move to london", are you talking about a future possibility? is it possible that he move to London??? or are you talking about a present unreal situation???
The correct form of the verb "to be" after IF, IF ONLY... is always "were". That is because they are followed by the subjunctive form. Even so, when speaking or in informal English, "was" is accepted instead.