Marriages in England and Wales could be by:
1) Banns
2) Surrogate’s or Common Licence
3) Special Licence
4) Superintendent Registrar’s Certificate
5) Superintendent Registrar’s Licence
Under (1) (2) and (3) marriages may be solemnized by a Clergyman of the Established Church of England in a licensed Church or Chapel of the Church of England, or, if by Special Licence, in any place and at any time.
Under (4) they may, as in cases (1) and (2), be solemnized by a Clergyman of the Established Church of England subject to his being willing to accept the Certificate in lieu of Banns; and under (4) and (5) by or before a Registrar of Marriages in a building of Roman Catholic or other denomination duly registered by the Registrar-General; before a Registrar of Marriages and a Superintendent Registrar in the District Register Office; or after the 1898 Act .(Marriage; Nonconformist Places of Worship), before a person duly authorised under the Act. Under this Act Roman Catholics and Nonconformists were not required to have a civil Registrar present.
If the marriage was by Certificate then it would be under (4) before a Registrar of Marriages in a building of Roman Catholic or other denomination duly registered by the Registrar-General. If the first marriage is not in the GRO Index then it could be there was something wrong with it, and it was not valid, and this is the reason for the second marriage.
J.B. Priestley's 1938 comedy "When We Are Married" is about three couples who found out that the minister who married them was not authorised to perform weddings.
Stan