Heya, I am pretty sure that the Milkstand described in the WCC heritage link below isn't actually the same milkstand that is on the corner here. As far as I know, there used to be one on middleton road opposite the train line. There also used to be a bridge crossing over the railway line from just next to nott house to this road. I believe this milkstand was destroyed about 5-10 years ago when a tree fell on it. Not sure if there exists a credible source for this though. 

https://www.wellingtoncityheritage.org.nz/buildings/151-300/211-nott-house-and-milk-stand-adjacent-to-middleton-road?q=