Q. Does Jewish law recognise common law unions?
According to rabbinic interpretation (Mishnah Kiddushin), there are three ways to create a marriage – giving the woman an object of value (kesef), giving her a document (sh’tar) and cohabiting with her (bi’ah).
All three require legal formalities. The long established practice is the first, kiddushei kesef.
While cohabitation was originally acceptable and is not prohibited by the Torah (Nachmanides’ explanation of Maimonides’ Sefer HaMitzvot, Commandment 470), the rabbis frowned on it.
Not only did they say that legally wedded wives have kiddushin and k’tubah whilst concubines have neither, but they argued that living with a man without marriage encourages licentiousness.
The verse, “when a man takes a wife” (Deut. 24:1) is interpreted as meaning that a couple who wish to be man and wife should proceed by means of legally sanctioned marriage.
All this applies to a woman who was previously unmarried; a married woman is forbidden to live with or have sexual relations with any other man than her husband. There are additional considerations in the case of a couple who have a civil marriage ceremony.
On the whole subject, I recommend M Elon, The Principles of Jewish Law (material from the Encyclopedia Judaica), 1974, cols. 371-6.