Thanks I had a look but it doesn't actually answer my question about non conformist marriages being legally recognised as it only mentions Quaker and Jewish.
I'm not sure, but I have seen somewhere that if a marriage was 'outside' of the church, eg. a Baptist/Methodist Chapel. The local minister had to be informed so he could enter it in the parish records, and recorded as 'not of the church' or something like that.
I think in 1837 things changed when a civil registrar had to be present when a ceremony was performed on unconsecrated ground. And then actual marriage certs were then issued to the happy couple.
I'm not sure if I've answered your question, but 1837 seems to be a year that crops up all the time.