Most people think that, after they've been living with their partner for a couple of years, they become 'common law husband and wife' with the same rights as married couples. This is not the case. In fact, couples who live together have hardly any of the same rights as married couples or civil partners.
British law != UK current law but those laws that in the distant past were direct descendents of UK law at the time.
British law vs say Roman law.
Because of the widespread nature of the British empire remnants of these laws (and remnants of the Empire, such as the Queen being formally the supreme being in Canada) are still found all over the world, even if a lot of those laws have been abolished in the UK itself.
I think you mean English common law. There's not such thing as "British law" as such, because Scotland has its own legal system (which incidently is partly based on Roman law).
The law varies from jurisdiction to jurisdiction but here in Ontario, common law status has very real consequences. Not all of them are bad and in fact if you read this FAQ on property division, it sounds like what people would expect when two people break up (e.g., joint assets are divided in half, each person keeps what belonged to them solely, etc.). Common law partners are also eligible for spousal support upon separation. People think I'm weird for not wanting to live with a girlfriend, but common law status creeps up fast and often before people have had the time to realize if the person is right for them in the long run.