Hi
I came across this on a google search and am not sure if anyone is still looking for any information.
The James Brunlees (or should that be Sir James Brunlees) is my 3x great grandfather. Argyle Lodge in question was on Parkside.
We have tried to do a bit of research on the house itself and have found the following,
The house was demolished after WWII and created into Flats (although from google street view I think the origunal entrance may still exist in the wall). Prior to WWII the house was actually split into flats and called 68 Wimbledon Parkside. This last appears in the electoral registers in 1953.
I've attached two articles that my father found in the times regarding the house.

This one is the notice of sale that we believe to be after 'Sir Jimmy's' death

This from the sale we possibly be from just before it is split into flats and includes a picture giving you some sense of the size of the house.
http://www.maps-of-london.com/map-wimbledon.htmThe link is a old map of Wimbledon from c.1940 and the house is still on there then so I think the map is a little bit older than the website says. It shows the sort of land that the house had. I’m sure there is a older map out there as well that has the land for each house plotted to.
Hope this all helps and if you want any more info on Sir Jimmy at all please just let me know.