For a real eye-opener of an article, from the Guardians Comment is Free section, do have a look at this.
What Muslims get up to in their mosques and in their Sharia councils is, of course, completely up to them, but this story does have some important resonances for us Catholics.
When you get married in a Catholic church, the priest or some other person acts as an authorised person and registers the marriage in a marriage register provided by the local registrar of marriages. These registers have to be kept in a secure place, so that unauthorised people do not get their hands on them and falsify the records. The same goes for the certificates of marriage. Every now and then you read in the papers of dodgy clerics who do weddings of convenience, mainly for would-be immigrants. When caught, these clerics get sent to jail.
As far as I am aware, it is illegal for a Catholic priest to conduct a wedding service for a couple who are already married. When a couple, married in a registry office, wish later to marry in church, then the Church does provide for what is termed convalidation, but these services are done in private.
Now, it is logically possible, I suppose, for a Catholic priest to marry a couple in a purely religious ceremony, and I have heard of this happening in France. Lets say an elderly widower wishes to marry; under French law his wife would then stand to inherit a set portion of his fortune. In order not to damage the inheritance prospects of his children (and if the prospective bride is herself a woman of means) he may choose to marry in church only, which of course would have no standing in law.
Funnily enough, I was once asked to marry a couple in a religious ceremony only. They were both on benefits and stood to lose their benefits (or some of them) if they married. For an unrelated reason I was unable to marry them, but I am pretty sure that this sort of wedding religious only, without civil registration is illegal from the point of view of canon law.
The whole thing is a bit of a minefield.
Sara Khans article highlights the problems of what is effectively cohabitation with religious blessing but no state sanction. If you have a religious wedding only you are not married in the eyes of the state and do not benefit from all the advantages that the married state brings. Incidentally, this was the case in penal times, when Catholic marriages were not recognised. That is why when Mrs Maria Fitzherbert married the Prince of Wales, she did so before an Anglican vicar: thus her wedding was completely legal, and the Hanoverian authorities later went out of their way to destroy the evidence for it.
It is not entirely fanciful that we may return to those days when Catholic weddings are no longer recognised by the state; but in that case, what would happen is that we would have the French and Belgian system: Catholics who wanted to marry would have to undergo two separate ceremonies, one civil and one religious. Whether that would be a good thing or a bad thing, I am not sure. I have heard some priests say they would welcome it.
Incidentally, there is nothing to stop mosques being registered for weddings, and imams becoming authorised persons; nor for that matter is there anything to stop Muslims getting married in registry offices either before or after their religious marriage ceremonies except of course in cases of polygamy. As I say, the whole thing is a minefield. And one has the idea that it is going to get more complicated in future.