Is ''secular law'' a recognised legal term or is that just a Stalinist fantasy?
Are you saying that a marriage is only legal if a secular humanist says it is?
In this context the term 'secular' law is used to make a distinction with 'religious' law (or Canon law in the case of Christian organisations). So secular law is that enacted by the UK government or its devolved bodies, such as Scottish parliament etc. It is, of course, a very well accepted term. Call it the law of the land, civil law, government law - whatever.
Religious 'marriage' only has validity if it is authorised by and conducted according to the secular law, law of the land, civil law, government law (delete as applicable to select your favourite term). If someone participates in a religious 'marriage' ceremony that is not authorised by and conducted according to the secular law, law of the land, civil law, government law (delete as applicable to select your favourite term), then they aren't married - simple as that.