It is possible it could be a late registration, but they are quite unusual, especially after such a number of years, and by far the most likely explanation is a re-registration. The timing (1927) suggests that is the case.
Finding the birth registration in 1904 could be difficult, because it could be indexed under a number of names, depending on the marital status, and surnames of the parent(s) named at the time. If you don't want to post the names here - I'm happy for you to send the details via PM and I'll have a look for you.
Were either of the parents, named in 1927, married to other people in 1904 ? If they were that may make a re-registration less likely (assuming they told the truth).
I have just been reading about late birth registration on another forum, and a contributor suggests that the Registrar General would take a baptism certificate as proof of the original birth. Otherwise how would you prove when a home birth had actually taken place?
The word, or possibly signed statutory declarations, of the parents could be enough - but a baptism certificate might be part of the evidence that could be submitted (but it wouldn't be a legal requirement).
Was it not considered breaking the law not to register a birth post 1837 in England ?
No - it is a lot more complex than that, but a simple failure to register has never been an offence.