"Living together as man and wife" means actually living together under the same roof and being in personal relationship.
Therefore, to prove "not living together as man and wife" it is sufficient to prove that the pair either or both 1) are not living together; 2) are not in personal relationship.
What evidences "being in personal relationship"? Shared budget, joint ownership of bank accounts/property, mail addressed to the two names, travelling together, being seen going out together etc. Having regular sex together is also a good indicator, though it may be difficult to prove either way. So, if none of this happens, it is a good indicator that the separated are not living together as man and wife.