My grandad used to sing it to me.
I always assumed it was a Lancashire folk song (that's where the "sav'ery duck" or savoury duck comes in - it's a traditional Lancashire dish and can still be bought at Bury Indoor Market, on the food stalls, along with Rag Pudding (steak in gravy wrapped in suet pastry) and the famous Bury Black Puddings.

He sang it as:

Oh me father died a week ago and left me all his riches:
A lump of Chuck and a sav'ery duck and a pair of leather britches
A teapot without a spout
A jug without a handle
A pepperpot without a lid
and ha'penny farthing candle
Oh knock at the door, ring on the bell,
see what you give me for singing so well...

Lancashire was pretty poor too, maybe it was used by some as a begging song?