At the moment I have begun reading this book. Amazon.com: Crimea: The Last Crusade (Allen Lane History) (9780713997040): Orlando Figes: Books
The backdrop to the war was the military pressure on the Ottoman empire by Russia in the 19th century. This caused grave worry to the British and French. The British worried the Russians might advance all the way to the Indian Ocean while the French worried about Russia dominating the Mediteranean.
Religious prejudices played a part also. Militant Catholics in France were outraged at Russian opression of Polish Catholics. Also a dispute between Catholics and Orthodox developed over control of Holy sites in Jerusalem. In England Protestants regarded the Orthodox as even more backward and superstitious than Catholicism. This led some low church Protestants in particular to regard Muslims as superior to the Othodox Christians. One speaker at a meeting in England insisted that Muslims were really a type of Unitarian.
Particularly interesting is the parellels with modern events. One British diplomat in the 19th century advocated the British taking over Mesopotamia to prevent Russian advance to the Indian Ocean. He said the country could be ruled easily enough by playing off the Shias and Sunnis against each other. In the decades before the war the British had also run guns to Muslim warriors in the Caucasus to try to stop the Russian advance, which is an interesting parallel to events in Afghanistan in the 1980s. In 1839/1842 the British invaded Afghanistan to control the country and prevent Russian penetration. The invasion turned into a disaster with nearly all the troops killed.
The most strong advocate of war was Lord Palmerston the former foreign secretary of Britain. He hoped for nothing less than a major war which would permanently reduce the power of Russia.