I think that’s what this building is called. Maybe Kensington Gore is the curved road which this buildings stands on. Google Maps suggests that Kengington Gore refers to both the building and the “thoroughfare”.
One of the most disagreeable features of Modern Movement architecture in and around the 1960s was its aggressive unwillingness to accommodate itself to the already established street pattern. Instead, higgledy piggledy streets at funny angles was bulldozed and replaced by rectangularity. Happily, those days are gone, and we are back to buildings being strangely shaped because the site is strangely shaped. Like the above pre-Modern-Movement edifice, which is now a favourite London sight of mine. I now visit the Royal College of Music quite a lot, to hear GodDaughter 2 sing or to be at some other event that she has arranged for me to attend. Every time I go there, I walk along Prince Consort Road, and there this Thing is.
I have only done a little googling, and so far I don’t have an exact date for when this Thing was built. Late Nineteenth Century is the best I can do for now.