Well, I hope I'm not treading on any toes by actually adding some reviews to this thread! None will be bad, because either they are all useful in different ways or else I can see they will/would be at a different stage in my learning.
I've been learning for a couple of months, on my own so far though I am now in touch with the WCCP and will be going to their January meeting. I have itchy book-buying fingers so have accumulated a pile of tutors. That I can even say that is amazing - when I first tried to learn concertina about 20 years ago, I went for the Anglo partly because there seemed to be so few resources for the English.
I started with Roger Watson's Handbook for English Concertina, so I'll start by reviewing that one. That was all I could find 20 years ago when I was trying to decide between Anglo and English, and it was all my local music shop had on the shelves this time round, so I bought it again. No doubt the old one is in the loft somewhere - probably with the old Black spot melodeon I never learned to play and either sold or packed so well that now I can't find it<g>.
This one fills the bill in that it gives you what you need to know to get started. The pages of chord shapes at the beginning are a bit scary for a beginner because it doesn't explain that you don't need to learn them at the start! It starts you right in on proper music with a C version of Winster Gallop which I like. It doesn't tell you much if anything about using the bellows - I was sawing away like on an Anglo to begin with, and using the bellows to control the length of notes too much. It doesn't have much in the way of music at each level, so you would need to supplement it with other simple music but in these days of internet downloads etc that isn't a problem. I wanted to learn carols for Christmas so downloaded PG Hardy's Christmas tunebook.
It's not my favourite, but it was there when I needed it and it does a good job so long as you have other music to broaden your practice.
Must work now! More another time....