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O! It's very possibly.

Without words. :)
Here scan from B.Schroeder.

As I wrote above, may be, L D Englis.

I know this article. But why do you feel that I.Barber may not be John Barber? There is an example of the John Barber razor with classic stamp in this article.

And now, in the Bill Schroeder book I have found one more I.Barber, he used logo "L D Englis". And comments "Very old very crude".

The history have a lot mysteries.:)
From "History of Yorkshire", Jan.1822.

http://manah.strazors.com/history_1922.jpg

From "Post office directory of Sheffield", 1854.
...

You are right. Isaac Barber was in business with James Barber (1894 - 1944). But according books only John Barber (1810 - 1834) marked his razors I.Barber.
And the blade form corresponds to period...