Viyella actually began as the world's first trademarked fabric, first woven in England by William Hollins & Co in 1893 from a blend of 55% wool and 45% cotton, in a twill weave. The name is from one of the main roads near the Hollins factory - the Via Gellia. Viyella grew in popularity quickly due to its durability and 'unshrinkable' quality, and was suitable for clothing such as winter shirts and pajamas. The fabric became associated with the upper and upper middle class in Britain, as it didn't come cheaply.
As Viyella began as a particular fabric, the name became a brand of its own, and so Viyella shirts are not necessarily made from Viyella - no new Viyella products are actually made from Viyella fabric, since it is no longer produced, having been replaced by a modern "Viyella" blend of 80% cotton and 20% wool.