Surely you aren't referring to this link, which you posted earlier:
https://www.ons.gov.uk/economy/envi...isthedifferencebetweensexandgender/2019-02-21
It doesn't actually contain any definition of "man" or "woman".
It contains definitions of "sex" and "gender", and notes that people might see themselves as man, woman, or somewhere on a spectrum between them, but it doesn't define the terms.
ETA: I think, reading the link, one could infer that they probably mean to use the definition, "A man is a person who expresses the male gender role". Similarly for woman. The problem with that definition, first put forward in these threads by Earthborn, is that either it is circular, and therefore meaningless, or it is offensive, because it asserts that men with feminine attributes aren't really men, and likewise for women. The only alternative reading of the article in the link is that it is not based on how you behave, but as how you identify, so we end up back to a woman is a person who identifies as a woman.
So, in summary, there is no actual statement of a definition of "man" or "woman" in the link. To the extent we could infer an intended definition, the definitions suffer from the same flaws as every other non-biological definition, i.e. circularity or inaccuracy.