After the 'melodeon playgroup' I switched tactics a bit. Prior to that I had just played a wide range of tunes from Paul Hardy's Christmas tunebook by trying to follow the dots. I largely played anything that I could recognise the tune for. However, since the 'playgroup' I've been trying to focus on a smaller range of tunes, and try quite hard to learn them.
I thought that I'd just learn one or two tunes, then once I had those sorted I'd learn some more, but I've carried on practising some other tunes, from a reduced list. I've started to find that I begin to be able to play a couple of bars from the tune from memory, so I add it to my list of things I am learning. I'm still largely leaving the bass end of things alone because except with 'Twinkle Twinkle', I find that trying to work out the bass makes me completely forget the other end. I'm planning to make a more concerted effort with the bass end over the Christmas break - hopefully, by then I will have a few tunes fairly well learned.
Tunes I can 'mostly' make my way through without any major problems: "Twinkle, Twinkle"; "Donkey riding"; "Speed the Plough"; "Skye Boat Song"; "Winster Gallop". I might have to slow down a bit on some sections while I remember where I have to go next. However, I don't really feel that I have completely learned them yet.
Tunes I can remember some bits from: "Polly put the Kettle on"; "Ding Dong Merrily on High"; "Kafoozalum"; "In the deep mid-winter"; "Cock of the North"
What's still on the list: "Shoe the Donkey"; "Keel row"; "British Grenadiers"; "Portsmouth". I can remember very short sections of these - a bar or so.
I know that I need to spend more time looking at the couple of tutor books (and Ed Rennie's DVD) that I have, but I tend to pick up the box when I've got a couple of minutes spare, which results in me trying to remember the tunes I do know.