But you agree that those happening in church or between believers were not marriages but 'marriages'.
To repeat until I am blue in the face:
Religious marriage is valid when it is authorised by and conducted in accordance with the civil law of the land (or secular depending on your choice of term). If not then it is not valid - simple.
Religious organisations recognise this, which is why, if possible, they ensure their premises and officiants are authorised under law to conduct valid marriages. And if not they ensure that couples include a civil ceremony as part of the process, because not to do so would mean they weren't married.
And couples recognise this too, which is why loads of couples have to go through a separate civil ceremony as part of the process - they realise that if they don't, well they won't be married.
So to put it simply:
1. Civil ceremony without a religious ceremony - married.
2. Civil ceremony with a religious ceremony that isn't authorised under law - married.
3. Religious ceremony that is authorised under the law - married.
4. Religious ceremony that isn't authorised under the law without a civil ceremony - not married.
Simple - strange that you seem unable to grasp such a simple concept, which is completely recognised and accepted by religious organisations in the UK.