If it shows "per (or by) declaration" in the informant column, it means that the informant went to a registration office somewhere outside the registration district where the birth took place to give the information. Instead of signing a register entry they would sign a declaration form, with all the information needed for the register, which would then be posted from that office to the registrar in the correct district.
The two days reflects the time it took for the declaration to arrive at the correct district and the information to be entered in their register.
There is a further puzzle in that it names a father - he has the same surname as the mother. However, in the section which asks for the name of the mother there is a maiden name.
I'm not sure exactly what you mean by this - it sounds normal (feel free to send me the details by DM if you wish), but if the mother is the
only informant, and the father is named on the entry, then she was claiming that they were married.
