I play piano accordion, English concertina, Anglo concertina and melodeon (amongst other things), and I would recommend the Anglo as being the better choice for Morris music, as it is far easier to play more than just the straight melody on one.

As we have a few musicians who play melodeon in our side, I tend to play either accordion or Anglo, though I do prefer the English for 'Second Morris (Badby)'.

I'd say the Anglo was as near as you're likely to get to a concertina with chord buttons, too - although the English 'chord triangle' method seems straightforward on the face of it, the reality is it can be rather complex because of the less than ideal placement of some accidentals (muso-speak for sharps and flats!).

In simple terms, a triangle may give you a major chord or a minor chord, it isn't a fixed pattern as such.

Wheatstone originally designed the English to make reading music easier - the notes on the left are one the lines, with the notes on the right in the spaces... then it got complicated!

At least with the Anglo, if you stick to the 'home' keys, holding buttons down on the same row will give you auto-chords to some extent, a bit like the bass end of a melodeon.