"they had been married very quietly at the Savoy Chapel"
The Savoy Chapel
Creative Commons AttributionThe Savoy Chapel - Credit: Elliott Brown, Flickr

The reason for Rex Mottram's and Julia Flyte's rather low-key wedding is explained later in the novel.

The Savoy Chapel, or Queen's Chapel of the Savoy, is situated off the Strand in London.

It was a chapel where a marriage without banns could take place, that is, a marriage which had not been publicly announced in a Christian parish church prior to its taking place.

The significance of this will become clear.