Ah, there's a fundamental difference between the E&W set-up and the Scottish one, explained well here: www.gla.ac.uk/schools/socialpolitical/research/economicsocialhistory/historymedicine/scottishwayofbirthanddeath/marriage/
In Scotland, the marriage is the agreement between the parties. It can take place anywhere, and it can be an irregular marriage with no celebrant. The marriage is then reported to the Civil Registrar so the parties get a convenient piece of paper and record of the act. Scottish marriage certs have a date of marriage, and a registration date sometimes a few days later when the paperwork reaches the register office.
In England (sorry, don't know much about Wales), the Church of England ceremony WAS the legal marriage. The CofE had a privileged status and people such as most Non-conformists had to rock up at a C of E church to get a legal marriage (I've seen a Methodist Minister married in an Anglican church by Anglican rites). Civil Registration was introduced in 1837 to allow people a legal marriage without going to the CofE. But it remained the case until recent decades, that legally the ceremony by the Methodist or Catholic or Muslim celebrant was just a nice piece of theatre, which the Civil Registrar would attend and then carry out the legal part of the marriage.
Hence these two consecutive entries in the 1837 marriage indexes for Lancashire:
HALLIWELL John MOLYNEUX Jane Preston Register Office or Registrar Attended Preston PRESTON/1/4
HALLIWELL Joseph CHAMBERLAIN Alice Bolton, St Peter Bolton 18/1/213
John Halliwell married Jane Molyneux either at the Preston Register Office or at say a Wesleyan chapel.
Joseph Halliwell and Alice Chamberlain had a CofE wedding at St Peter's church, Bolton.
Over the decades, more and more religious celebrants have been recognised for conducting a legal marriage. I think Catholic is now on the privileged list, but am not sure of Muslim. (Jewish & Quaker ceremonies have had a special status since before 1837, but I don't know much about that.)
So it's very easy to incorporate Humanist weddings into the Scottish registration system, which was designed from the start to incorporate plurality. While in E&W it requires immense huffing and puffing and legal change, and gives the CofE bishops in the House of Lords the chance to stamp all over it. Essentially the E&W system is designed to perpetuate the privilege of the Church of England.