The earliest use of the term “penny whistle” attested in the Oxford English Dictionary is from 1730, in the play Bays’s Opera by Gabriel Odingsells.
Musicians with Halters about their Necks — Their Instruments strung behind, penny Whistles, Trumpets, and so forth, in their Hands.
This doesn’t tell us what a penny whistle was but clearly refers to a musical instrument of that name. It is similarly uncertain what the name designates in the review of a performance at the Covent Garden Theatre, in the 22 September 1809 issue of the London newspaper The Morning Chronicle. An announced increase in ticket prices triggered an organized wave of disruption throughout the event.
A pause of some minutes ensued, and then the cat calls, bugle horns, and posthorns began discord afresh. … This was succeeded by the usual concord of sweet sounds proceeding from penny whistles, squeaking trumpets, watchmen’s rattles, horns, catcalls, &c. &c.
A letter to the editor in the 9 September 1810 issue of The Examiner complains about the noise caused by street criers.
… persuade them, if instrument they must have, to change the hoarse window-shaking and nerve worrying mail-horn, for the light and softer cadence of a penny whistle.
The 15 June 1818 issue of The Huntingdon, Bedford, Cambridge and Peterborough Gazette and Midland County General Advertiser, notes the following about the visit of a contentious politician.
… he entered the town amid the braying of trumpets, the beating of drums, and the shrill piping of fifes and penny whistles …
Compilations of Irish and Scottish traditional music began to name the flageolet shortly after the initial printed evidence of its English form (discussed in the preceding post along with its proximity to the fife). The first such collection I know of was published ca. 1804.