The book The Burning Tigris: A History of the Armenian Genocide by Peter Balakian is a detailed account of the Hamidian massacres of 1894-1896, the Armenian genocide and the reactions by Britain and the United States to those events.
Balakian cites contemporary sources which gave estimates of the death toll in the massacres:
It was militarily possible for say Britain, France and Russia to have intervened. It was political rivalry and the fear by Britain and France that Russia would grab Constantinople that stopped them. But presumably Russia could have intervened through the Caucasus.
It's simply not true. Lepsius didn't see any massacres or victims himself, he only had hearsay provided by Armenians, and saw only places Armenians took him too. From that he extrapolated. He was a pastor, not a statistician, and it is physically impossible for 250,000 Armenians to have been killed, let alone 100,000. We have census data from before the massacres, and census data from after. There is no 250,000 gap.
Almost all contemporary sources agreed that the number was about 15,000.
However, that doesn't matter, as 1 Christian killed is enough for a Western intervention. After all, in the Greco-Ottoman War of 1897, the Ottomans were responsible for exactly zero civilian deaths in a war that they won against Greece which had invaded the empire without cause or declaration and massacred large numbers of Muslims, yet the Powers took Crete and gave it to Greece.
However, in the case of the Ottoman Empire, there was no real way to intervene without Russia, and all the gains would be Russian.
The British couldn't really do much, except maybe bombard ports, which would end up killing large numbers of Christians, and it would all be photographed.
This might have been an opportunity to partition the empire, but that's a step that even Salibury feared to take. If perhaps Abdul Hamid II had been killed in one of the constant stream of Armenian terrorist attacks, that might have led to political chaos that might have prompted Britain to participate in a partition.