I'm not sure how common it is for small monuments to be listed (other than when they're part of a listed property or conservation area), but our war memorial and the bronze plaque behind it have just been given Grade II listed status. As they're situated in the Memorial Gardens, I don't expect they were under any threat, but it's probably good to accord them protection.
The reasons include the historical and architectural interest, including the fact that the 1921 cross is "an ornate example of the oft-used market cross style of memorial with well executed Arts and Craft influenced floral and Gothic tracery".
So next time you're in the old town, maybe you will appreciate it even more.