apologies m - I copied from Reynolds, who has written 336502 - Thompson, Gulliver and Slack all show the No. correctly as 366502 - why did I pick the wrong author to quote (though he shows the correct date of Registration). So, if anyone has Reynolds book, you might care to change the Rd. No. for 'Fibrillose' to read 366502 - page 74 Appendix B.
As a matter of personal thought, I don't see this Registered Design as being remotely like herringbone - what I see is a random applied trailing without any recognizable pattern. The odd thing is that Reynolds says of this invention ......... "In 1901 J. S. Williams with John Northwood developed this interesting glass making technique ................ etc. " quite how that fits with the fact that the Company had already Registered Fibrillose the year before seems a bit odd.
Sorry, forgot to say that the bowl I've seen - matching your third linked item - is in clear and not green, unfortunately. This might work in my favour insofar as the rest of the public might not give it a second look

W/Fs seem to have produced most of their threaded pieces - threading similar in fineness to the pieces here - in the 1930s, and they seem to have used at least half a dozen different greens at one time or another, so difficult to be precise on that issue. Trying to stay on topic for the OP, since I've digressed too much and coming back to the OPs bowl, it's the waisted shape of the bowl that give most problems when comparing to Jackson and the big book. Perhaps from a fashion point of view, the factory appear to have avoided such an outline shape during the time they were producing threading, and since attribution relies heavily on sourcing provenance from factory catalogues and books - and I can't find anything that matches this shape, then it looks to be a dead end for the time being. It might be worth OX151 contacting the MoL and requesting their help with this one.
The 'James Powell carafe c. 1884' in the Barnsley Museum is, we assume, id'd correctly, and the use of trailing by the factory goes back before that date, though it has to be said that the threading on the carafe is very much out of character for the period in question - most of the material produced at the date suggested were the opal colours, styles from antiquity, and the odd tear or prunt. The threading looks to have more in common with the C20, but we won't argue with the museum.

It's always a problem with high end pieces when individuals or museums omit to provide provenance for their attributions - we tend to take museums at their word, but it would be very helpful to us collectors and wouldn't take any time at all, just to confirm the source of the attribution by providing a little bit of text.
Perhaps Anne (Mod.) might correct my error on the Fibrillose Rd. No. some time - thanks.