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They were used on the early Long Lees and the various ancillary models of the era, and never with the SMLE (introduced 1903) and all Lee-Enfields after it.
If you are referring to the canvas breach cover, then yes they were used into WW2. I've seen period photos with them installed on No4s, and I have a Canadian marked 1942 dated cover.
These are usually called bolt covers. They were fitted to Lee Metfords and Long Lee Enfields. On the MkI &I* LM they were retained by screws to the bolt. On the LM MkII&II* and Carbine and the LLE MkI&I* and Carbine MkI&I* the cover was retained by lugs and groove on the bolt. The cover was deleted on the SMLE because it would interfere with the charger guide.