Browsing a bit more at the Bodley with an expanded list of song titles, I found the lyrics to the following:

As Welcome as the Flowers in May (aka The Jolly Miller)
        I live at the mill at the foot of the hill
*Granny Snow!
*Jones' Musical Party
*Mary Ann, or the Roving Gardener
*My Old Wife. Harding B 11(2576)
Poor Old Mike
Put the Break [sic] On When You're Going down the Hill
There's a Smile Waiting for Me at Home
Water Cresses! Harding B 11(4046)
The Watercress Girl
*The Way to Be Happy
The Weeping Willer
Up a Tree
*The Young Man on the Railway (= The Mail Train Driver)

Steve Gardham has sheet music or scans for the starred items, which means I may be posting MIDIs and/or ABCs for them in due course.

"My Old Wife" uses the same music and nearly the same chorus as "My Rattling Mare and I," for which I've already posted music. Steve noticed this similarity, and theorized that it was a parody written after Clifton jilted his wife and took up with Fanny Edwards.

Note: Someone somewhere along the line wondered if "The Weepin Willer" was a Geordy parody of "Polly Perkins". Judging from my brief inspection, I'd say no.

I forgot to check the titles found in the HC Comic Songster, which I haven't yet incorporated into my personal list.

If anyone has music for these titles, aside from Steve's holdings, please send me scans! PM me for an email address.

Also, can some friendly soul Down Under scan the music to "The Adventures of Robinson Crusoe" in the National Library of Australia and send it along?