Click the tag I've added under your post. That should keep you going. But, in short, I think it's most likely to be for venting and access to the now culverted Stonebridge Brook.
Thanks for that info, remarkable that there seems no definite answer, as yet. I will trawl through the previous posts, thanks again
Well, I think the answer is pretty definite, but lacking in authoritative references!
I have always wondered about this structure, too.
Google aerial shows they are open flues at the top. Must say in umpteen years of riding and walking along Wightman Road I never spotted them. Even used the garage in later years!
That's right. I added a screenshot of that here, along with a picture of the tower in 1885 before it was built higher.