It has Provisional Birmingham Proof as applied to the rough tube in use 1855-1904. The '17' means the original bores were .649-.654, or tight 16g.
English Parkers include William Parker who was a gunmaker from 1790 until 1840 and one of the forerunners of Parker, Field & Sons, High Holborn, London, 1841-1876. E.D. Parker shotguns were listed in the 1895 Clabrough & Golcher catalog.
You might post in focus high resolution images of every mark on the barrels and flats here.
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