I have not encountered any grenade like this based on a Mills body. The example shown appears to operate by removing the pin and then rotating the top cap section, perhaps a quarter turn, to release an internal striker. Is that how it works? Are there other photos available to help clarify?
If the item does date from WWI, the closest patented idea may be one from James and Samuel Walster (No. 16749, application date November 1915), whereby a simple push in/locking fuze plug was suggested in order to expedite grenade production - the Mills-style lugs for lever and pin were dispensed with, removing steps in the maching process. Although the patent does not discuss a fuze in any detail, a simple twist mechanism retaining a striker and spring in compression would be possible. However, I am not aware that the Walsters actually produced any grenade prototype to their patent, so unfortunately all somewhat speculative.
Equally the item might represent a completely independent and parallel development carried out in the field. Where was this example found? The location might suggest British First or Second Army workshops... Even more speculative, so hopefully someone else might have some facts to hand.
Tom.