Some of the music is traditional - no one knows who wrote it and it's been around for centuries. There's also quite a lot written in the old style by known composers and the production of new music for dancing seems likely to continue. Some of the music isn't even English in origin and sources include other parts of Western Europe and the Americas. Some has been derived from Morris tunes probably because some of the musicians play for that too.
The Morris influence may be whyMelodeonsfeature in many of the bands but almost any instrument is "allowed". Here's a short list of instruments: fiddle, recorder, whistle, saxophone, percussion, clarinet, mandolin, guitar, keyboard, dulcimer ... Over the last 40 years, cheap and effective electronics has made it possible to accommodate almost any instrument.
A more extensive listing is here and these "search links" that will probably find more for you: