There is a lot of information if you Google.
Yes - I have Googled, but I'm not sure I really know the answer. That's why I've posted here. I hoped someone with knowledge and expertise on Gibraltar would be kind enough to share their wisdom with me.
I've been able to rule out some barracks because they didn't exist until after the date I'm looking at.
I'm glad I've been able to narrow it down but I'm still reading about references to Lathbury Barracks, South Barracks, Buena Vista Barracks and Grand Casements Barracks (used into the 1950s, I believe). I've probably missed some.
The point is, I've learnt about lots of barracks, but I still don't know the answer to my question. That's why I asked for help.
Do you know the answer yourself? If you do, it'd be nice if you shared it with me.