I think I figured out now what may have happened.
There seems to be no matching Moore-Brett marriage,(at least not in England).
Officially married or not, female Moore is known as mrs Brett (maybe she also had children named Brett). He dies, or they split up, but she still uses the name Brett.
She meets Hurley, and is then known as mrs Hurley, formerly Brett. They have a child. For some reason they don't/can't marry (one or both still married?) therefore just the mothers name: Hurley, otherwise (or formerly) Brett.
When they marry they set things straight: she marries as Brett, formerly Moore. And consequently, her name is that on the re-registration of their child.
If the child would later apply for a birth certificate, giving date and names, the second one would automatically be sent because of the reference on the first one. No sign of illegitimacy there, she wouldn't see it and nobody else.
In our research we order certificates with Vol and Page numbers, which may be the reason why we can obtain the first one, especially if we order both at the same time?
So much for privacy and protection!
Christine, I never knew about these re-registrations at all, until a few weeks ago, and now I'm surprised and quite shocked to read that they could already re-register as early as 1927. I'll send you a PM why.