The United Kingdom is due to leave the European Union on 29 March 2019. Current guidance from the Home office with regard to the situation after that date is that it is not intending to make changes immediately post Brexit to the way European Economic Area (EEA) and Swiss nationals are able to marry in the UK, though the situation may change in 2020 following consultation with all interested parties.
This means all EEA nationals can continue to be married by Banns or Common Licence for at least the remainder of 2019, assuming the couple has a legal link to the parish or church, either under the Marriage Act 1949 (residence in the parish or membership of the Electoral Roll of the church) or the Marriage Measures 2008 and 2012 (by way of qualifying connection).
For further guidance on this (and on qualifying connections), Deanery information leaflets are available to download and can be found in the Document Library under the Information tab.
Further information will be provided as soon as it becomes available.
Guidance on all legal matters can be found in the legal section of the Diocesan website (https://www.oxford.anglican.org/support-services/legal-diocesan-registry).