Perhaps someone who knows more about India during this time can give more thorough explanation, but it's basically presentational dress for formal occasions. It would likely have been required attire for certain government events. I found a similar ensemble being worn by Lord Louis Mountbatten to meet the Maharajah of Jaipur. It's heavily inspired from early 19th century uniforms, like what Sir James Rivett-Carnac, wore in 1840 while Governor of Bombay.

I also looked into the tailors a bit. They aren't a particular famous shop, but they had a fairly long brand life. Seems "Cooling, Lawrence, & Sons" became "Cooling, Lawrence, & Wells", eventually "Wells & Sons", and finally "Wells Tailors and Shirtmakers". This brought them through to the 1970s in that location. In their initial form, from 1907 to 1955, they specialized in uniforms. It looks like the London College of Fashion has a collection of that companies paperwork in archives, both time sheets and a livery sample book. There's a good chance the records might contain some mention of the uniform in question.