This looks possibly relevant.
From Jackson's Oxford Journal, 12 May 1855
City Court, Friday May 4
Charles Higgs, a painter, was committed to take his trial at the next Assizes, on a charge of making false statements to the Deputy Register [sic] of Marriages, and by that means procuring a solemnization of matrimony. Mr G Brunner presented, and Mr Mallam defended.
So the "solemnization of matrimony" in question took place in a register office or nonconformist church/chapel, rather than an Anglican church which would not have required the involvement of a Registrar.