There are many opinions as to the ideal diameter for English Horn tube cane.
Any discussion of the "ideal" diameter of tube cane must also take into consideration other factors besides the gouge and shape used. The elevation, humidity and temperature during various seasons and the overall climate are just a few other things to consider. Another factor is the hardness and/or graininess of the cane.
On numerous occasions, I have been asked about the diameter of cane I prefer to use. Since I use a shape that is on the wider end of the spectrum, I prefer tube cane with the diameter of 12 - 12.5 mm. Cane with a larger diameter than 12.5 mm has never gouged well on my machines and the openings of the reeds have been too closed. Conversely, it has been my experience that cane with a smaller diameter than 12 mm has resulted in tip openings that are larger than are comfortable to play. However, if one is using a narrower shape, a diameter less than 12 mm can produce reeds with a tip opening that may not be too large to control. In any case, I would avoid cane with a diameter less than 11.5 for English Horn reeds. Instead, consider using it for oboe d'amore reeds.
It is important to know the size of the bed of the gouger in order to avoid gouging cane with too large a diameter for the machine. If gouging your own cane, that information should easily determined by measuring the bed. Any gouger manufacturer should be able to give you specifics, as well. However, if one has purchased gouged cane, it can be more difficult to obtain this information. Contact the dealer from whom the cane was purchased and ask specific questions about what gouger was used, the size of the bed and whether the cane was gouged wet or dry.