I also looked in Nigel Brown's books on British Gunmakers for more information and he seems to have omitted to mention Cook. Odd, with the fact he is in Bailey and Nie. The Thomas patent snap action had a brief popularity and faded out around 1873 with few guns after that date showing this patent. Patent date was April 1870 and as you know the date it came across it really narrows it down quite well. I would very much doubt that any information still exsists. A good source can often be the local museum. I have come up with this link which might be worth a try:
http://www.sheptonmallet-touristinfocentre.co.uk/activities.php?venue=radstockmuseum Nice gun and in good condition for its age. Black powder proof only by the way. Lagopus.....