I've never seen a customized Baikel single barrel gun before. Actually it looks quite nice. I had one in excellent condition that I was forced to take in with a gun that I wanted. I paid 20 for it and eventually sold it for the same.
I mentioned the BSA Snipe as a hammerless single. They are a bit crude in some ways but were reliable. The worse single machine made English gun was the Argyle (there will now be a few groans from English readers) with springs that we worse than those in a small mouse trap. I would think it hard to give one away here unless it was in mint condition and someone wanted one as a curiosity. The Greeners were quite heavy and built like tanks but will last several lifetimes; there was even a multi-choke version. Midland Gun Co. did sell a single known as the Hammerless Knockabout. I have only ever seen on and that was a 16 bore and had German proof marks. Bernadelli in Italy did make a single hammerless folding gun that was very light where the opening mechanism was by sliding back the trigger guard. There are few quality English single hammerless guns but they are quite rare and usually command a good price. If you could find one of those it would be an absolute gem. Lagopus.....