It's an intriguing puzzle Rod!
Yes, sorry, of course I meant that the stamp had been used
postally!

I wrote that in too much of a hurry before going out.
I agree that it's not clear whether there are four or five bars at the top.
George Brummell wrote in his 1946 book in the context of discussing England and Wales duplex postmarks that he knew of the following postmarks with five bars at the top and bottom:
HULL - 383
GRAMPOUND - 671
SOUTHAMPTON - 723
ALEXANDRIA - B01
where this Alexandria is the one in Egypt
and also LIVERPOOL (I assume 466) with the name horizontal.
I guess the mark is probably from a duplex, either type G Duplex (name curved) or type H Duplex (name horizontal) using the terminology of Collect British Postmarks.
I suppose though that it could be an older type B (vertical) single postmark.
The stamp was cancelled no earlier than 1881 when die 4 stamps were first produced.
This would be too late to be an Inland Branch D37 postmark as this block of D numbers was last in IB use around 1870 according to Parmenter & Smith (on the GBPS website).
Coggeshall was listed as D37 in the 1882 official post office list so I think it's a possibility.
It's not clear to me how many different hammers may have been issued over the years to a single office (to to different offices when the post office number was re-assigned).
However, it would be satisfying to find an example of one that matches the postmark on this stamp.
I see the following postmark types for "?37" offices in Collect British Stamps lists the following (including only England & Wales types B, G & H) where the dates seem possible:
137 - Broadway - H
237 - Dartmouth - H
337 - Harlow - B, H
437 - Kirkby Stephen - H
537 - Morpeth - G, H
637 - Reigate - B, G, H
737 - Broadstairs - B, H
also Broadstairs/Station Office - H
and Broadstairs/Station Office B.O. - H
837 - Reeth - B
937 - Barnet - B, G, H
037 - Castletown/Isle of Man - B, H
D37 - Coggeshall - H
G37 - Grosmont/Yorks - H
H37 - Horley Station/Surrey - H
also Horley Station Rd - H
J37 - Bramley/Surrey - H
K37 - Mumbles - H