Are you referring to a birth in the nineteenth century, or today? According to the 1874 Registration Act, although you could go to any office the registration was made in the district in which the birth took place, as stated in the Act;
6. Any person required by this Act to give information concerning a birth, who removes before such birth is registered out of the sub-district in which such birth has taken place, may, within
three months after such birth, give the information by making and signing in the presence of the registrar of the sub-district in which he resides a declaration in writing of the particulars required to be registered concerning such birth; and such registrar on payment of the appointed fee shall receive and attest the declaration and send the same to the registrar of the sub-district in which the birth took place; and the last-mentioned registrar shall, in the prescribed manner, enter the birth in the register; and the entry so made shall be deemed, for the purposes of the Births and Deaths Registration Acts, 1836 to 1874, to have been signed by the person who signed the declaration.
A person making a declaration in pursuance of this section in the case of any birth shall be deemed to have complied with the provisions of this Act as to giving information concerning that birth, and with any requisition of the registrar made under this Act within the said three months to attend and give information concerning that birth.
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