I just have to correct your misconception about "Roast Beef of Old England", which I have in many an old songbook: Fielding wrote it! It's "Hard Times" that was the follow-on version. Here's the Wikipedia entry on "Roast Beef":

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The Roast Beef of Old England is an English patriotic ballad. It was written by Henry Fielding for his play The Grub-Street Opera, which was first performed in 1731. The lyrics were added to over the next twenty years. The song increased in popularity when given a new setting by the composer Richard Leveridge, and it became customary for theatre audiences to sing it before, after, and occasionally during, any new play. The tune is also played at United States Marine Corps formal mess dinners, during the presentation of the beef.

The song provided the popular title for a 1748 painting by William Hogarth: O the Roast Beef of Old England (The Gate of Calais).
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The modern parody is "Hard Cheese of Old England" by Les Barker.