Did the USSR pose a threat to British India and to what extent did this affect British decisions early in the war?

As I read through various published NKVD reports on Russian letters written during the Winter War, several of them mentioned a belief held by the writer that the UK was unlikely to intervene in the Winter War or to declare war on the USSR in general, due to the perceived threat on British holdings in India. Did the USSR have an actual option to invade India through Central Asia or was this just something produced by the soviet propaganda machine? Did the UK believe that this was a possibility and did it affect their decision-making especially during the planned invasion of Norway and intervention in Finland?