Matthew: There are definite and quite narrow limits to what can be achieved on a 20-button Anglo. As Good Soldier says, you would certainly need more buttons to play Irish tunes, but if song accompaniment is what you want to do you'll need a range of chords, and a 20-button is limited in that respect too. As a teacher of anglo I would say that a 20-button is fine to get the idea of how the instrument works, but if you decide you want to continue with it, you need to upgrade to 30-buttons (not 26, as your chording would still be limited) as soon as you can afford it.

Richard is quite right to say that using alternative notes in a different bellows direction can allow different chording, but Peter Bellamy did very little of that. His style, though original and effective, wasn't terribly complicated technically. He did use drones a lot (specially adapted buttons on the third row), but he also played the tune most of the time along with those chords that came naturally, and these often clashed with the drone to give that dissonant sound so characteristic of his playing. I'm pretty sure he also added extra discordant notes by design. The point is, he played a lot of notes at once, and you aren't going to do that with 20 buttons.