There is no license from a magistrate in the UK for a marriage . If the marriage is not in a church and is to take place in a registry office a license is required issued by the registry office for that marriage . . A church wedding requires a passport or other identification ., proof of residence within the parish , a bill for example . A decree absolute for a divorced person which is all dealt with by the vicar or priest in charge of the Church . As a Foriegn national MM may have been required to have a license from a local register office as well .

I would dispute the stories of the wedding being a “sham ” .JD The Archbishop of Canterbury is the principal leader of the Church of England and the symbolic head of the Worldwide Anglican Communion representing almost 100 million people . The Queen is the Supreme Governor of the Church of England , in effect representing God here on this earth .
The First Archbishop of Canterbury was Augustine of Canterbury 597 ., there has been an Archbishop of Canterbury for 1400 years .
To suggest a “sham ” marriage would be sanctioned by the Queen as Supreme Governor of the Church of England and Justin Welby as the leader of the Church of England and 100 million Anglicans is frankly not possible , jeopardising a 1400 year. old institution for MM is too much of a stretch .

The record of of a Royal marriage is not legally required to be shown to the general public ., however it is a legal requirement for the marriage certificates to be signed, and these records belong to both the state and the Church.They will eventually be (historically )available ) A sham marriage would simply not be allowed . It would cause a constitutional political , legal and ecumenical crisis and could mean all marriages conducted by Anglican priests wordwide to be null and void . . The birth certificate is essentially a private affair , any marriage between a senior member of the RF is in effect state owned and is governed by both church and state .
The RF can do a lot of things but not this .