The first of these new chairs was brought to my attention by Rob Derrick, a dealer from Hay-on-Wye. Illustrated here, it is more or less identical to the two previously known chairs, having four spindles and the typically West Midlands timber seat. It's clearly marked with the initials WC in the usual places, on the tops of the back legs. Many thanks to Rob for contacting me about this, and for allowing the use of his photographs.
The second new chair appeared on the website of another dealer, and was brought to my attention by Oli Barling who saw it on Instagram (Thanks Oli). This chair is similar to the others in all respects other than having a woven seat. This would originally have been rush, but has been replaced by seagrass. I've asked for permission to use photographs of this chair, but it hasn't been granted, as yet - you can view it here as long as it remains up for sale.
I'm sure there are other William Cole armchairs out there, aside from these four. If you do know of any, please get in touch, and help take the research forward.