The English madrigals were a cappella, predominantly light in style, and generally began as either copies or direct translations of Italian models.
When Nicholas Yonge published Musica transalpina in 1588, it proved to be immensely popular, and the vogue for madrigal composition in England can be said to truly have started then.
Musica transalpina was a collection of Italian madrigals, mostly by Ferrabosco and Marenzio, fitted with English words.
While William Byrd, probably the most famous English composer of the time, experimented with the madrigal form, he never actually called his works madrigals, and shortly after writing some secular songs in madrigalian style returned to writing mostly sacred music.
Wilbye had a very small compositional output, but his madrigals are distinctive with their expressiveness and chromaticism; they would never be confused with their Italian predecessors.