The mistaken belief that cohabiting couples enjoy legal rights similar to those who are formally married or in a civil partnership. They don’t. There is no such thing as a “common law” wife or husband or marriage, no matter how long a couple may “live together as man and wife” or however one wants to describe it.
Historically, the expression was once used to describe the recognition, under the law of England and Wales, of marriages conducted abroad or under some forms of traditional or religious ceremony. But that is not its modern meaning in this jurisdiction. Its appearance on some legal-looking forms, eg from banks or building societies, is as anachronistic as the ubiquitous (but inappropriate) image of a gavel.
Cohabiting couples do not enjoy the same legal rights as those in a marriage or civil partnership. Most importantly, cohabiting couples cannot divorce in the sense governed by the Matrimonial Causes Act 1973, and their property, however shared, cannot be reallocated in the same way as happens on the breakdown of a marriage or civil partnership. Instead, their property is dealt with mainly under the law of trusts. There are other differences, too, such as what happens under the law on intestacy, if one of a cohabiting couple dies.
The courts’ powers in relation to children, on the other hand, are largely derived from legislation that does not depend on whether the parents are married or not, with some exceptions (eg in relation to the attribution of parental responsibility).
For a convenient introduction to the topic, see The Transparency Project’s guidance note, Common Law Marriage: the rights of unmarried couples and the myth of common law marriage