These preaching bands belonged to the Reverend Dr Oliver Soper, Baron Soper of Kingsway (1903-1998), one of the most commanding Methodist preachers of the 20th century.
Preaching bands are worn around the neck and are fixed with thin ties. Such bands are still worn today as part of clerical (non-liturgical) clothing by the clergy, and also by some members of the legal and academic professions. Preaching bands are a distant cousin of historic neckwear, such as cravats, jabots and ruffs.
See also Soper's portable preaching stand and other Soper artefacts in the Online Collection.