They simply had no capacity to control a country like India on the other side of the world in their state at the end of WW2, so might as well save as much face while they can.
It does seem like opposing nonviolent and violent factions who reject each other works better than just one.
Northern Ireland, Malcolm X/MLK, etc.
My opinion is that the fear of marxism permeating the civil right movement (especially the BPP) and starting to reach the Latino and disfavored white people (the "rainbow movement" if i remember correctly) did strike fear into the US government (hence the assassination of Fred Hampton, who really started this). This fear allowed to Civil right movement to be successful, because ethnic tension, while useful to exploit a minority, is not worth the danger to the social order.
Now imagine that instead of post-war British, the colonial regime were held by their contemporary Stalin. How much would a peaceful protest achieve?