Jenny:

"By yon bonnie banks and by yon bonnie braes" is a quote from LOCH LOMOND (click)--which is in our Digital Tradition database.

WITHIN A MILE OF EDINBURGH TOWN ("town" might be spelled and pronounced "toun" or "toon" in Scots) is another song that has been posted above in this very thread (click).

Of course, neither of these is the song you want, but they are both quoted in your song.

I can't identify your song, but I have a hunch it might be a "patchwork song", that is, a song made up principally of quotes from, or titles of, other popular songs of the day. This genre was once quite popular. See this thread: Lyr Add: Patchwork Song (1860s Pop) for a discussion and several examples.