These are notoriously difficult to identify precisely, but I do not think your s is for a trench mortar. Those tended to be normal cases with a shoulder.
Your example looks more like the “Detonator, No.22 Rifle Grenade, Mark I.L” which was a straight case inside which was a “Detonator No.8, Mark VII” , enclosed in a paper tube. The base was painted red and a normal ball headstamp was left on the case. A similar detonator with a straight case and base painted red was the “Detonator, No.39 Grenade Matk I.L”
Another round that used a similar straight case was the "Detonator, No.110 Fuze, Mark I.L and the following Marks II and III. However, the base of these was not painted red and the Marks II and III had black stained cases. They also held a detonator in a paper tube.
I am intrigued by the headstamp you listed. Is there any chance of a picture of it?