The Chinese Cheng, which was introduced to Europe in 1777, is generally credited with being the musical instrument that initiated the ideas that were used to develop the accordion.
In 1821, Haeckel in Vienna and then Buschmann in Germany, invented mouth blown instruments of the free reed family. Buschmann added bellows and a button keyboard in the following year to make his “Handaeoline,” possibly the first clearly recognisable forebearer of the modern accordion. In 1829, Demian added chords in the bass and patented this as an “Accordion”.
From 1830, Charles Buffet in Belgium and Fourneax and Busson in France, manufactured an accordion that had 10 to 12 treble and two bass buttons. Demian also manufactured a type of accordion he called the “Hand harmonica”. A tutor printed in 1835 (by Adolph Muller) listed six varieties of accordions, all diatonic in the keys of C, D or G. It seems that the accordion did not become chromatic in note range until about the 1850’s.
Wheatstone in England had invented his concertina in 1829 and he continued to develop it over the next several decades, but he did not attach a piano keyboard to it. Busson did, and called it the “Organ accordion”. By 1859 this had a three octave treble keyboard. Both the Wheatstone Concertina from 1844 and then accordion had uniform tone (ie were not diatonic or in one key only). It would appear that the development and popularity of the Wheatstone Concertinas actually slowed the acceptance of the piano type accordions in England, at least until the twentieth century.