Russia had been eyeing the Balkans for years. Its ultimate (though unrealistic) goal is to march into Konstantiniyye (Constantinople). From there they could control shipping through the Eastern Mediterranean.
Britain was worried that Russian expansionism would lead to 1) destabilisation of Europe and another war similar to the Napoleonic Wars, 2) threat against their own holdings in the Eastern med namely Malta, Ionian Islands and British-friendly regimes in Egypt and Greece, 3) fall of the Ottoman regime, which would threaten Med sea routes and the overland route to India. For more on the British foreign policy at the time, go here
http://www.victorianweb.org/history/forpol/principle.html
Russia began to style itself as "protector" of the southern Slavs of the Balkans against the Ottomans, as well as the "defender" of Christianity in the East. Conflict between Catholic and Orthodox Christians in the Holy Land came to a head, and the Muslim governor had to intervene to prevent Christians killing Christians.
According to this website:
http://www.regiments.org/wars/19thcent/53crimea.htm "The catalyst for war was a growing dispute from 1840s over the religious custody of Christian Holy Places in Palestine. Catholic monks under French protection had tended the Jerusalem and Bethlehem holy places since the sixteenth century, and this had been guaranteed in perpetuity by the Ottoman capitulations of 1740...Louis Napoleon, seeing the possibilities for political influence, sought reinstatement of the capitulations in 1852, and, after his coronation as Emperor, his concern about religion in the East became a rallying cry for French Catholics. The Sultan supported French claims of jurisdiction. Tsar Nikolai I objected that Russia was the true defender of Christianity in the East, that such a protectorate existed by the Treaty of Kuchuk Kainarji (1774), and that Greek Orthodox were by far the majority Christians (ten million) in the East. The dispute broke into violence in Jerusalem between Catholic and Orthodox monks, and the Muslim governor intervened in 1847 to prevent Christian killing Christian. More importantly, French imperial intrigues revived Russian proposals for dividing the Ottoman empire. The tsar secretly sounded out the British about dismembering the Ottoman empire, but the British, continuing Palmerston's policy of containing Russia, indicated they would do all they could to keep the dying empire alive."
From the same source: "In March 1853
Russia issued an ultimatum that amounted to a demand for Ottoman unconditional surrender: recognition of exclusive Orthodox Christian rights in the Holy Land, Russian protection of those rights, restrictions on other Christians who might interfere with Russian influence, and a new secret alliance to "protect" the Ottoman Empire from the French. The Sultan refused. In July Russia invaded the Ottoman Danubian Principalities of Moldavia and Wallachia. For five months the Turks held the upper hand, encouraged by a British and French naval show of force around the Dardanelles. When
in November the Russian Black Sea Fleet destroyed the Turkish fleet off Sinope, Britain and France were alarmed and sent an expedition to the East to protect the Ottoman Empire from Russian aggression. The eventual main object was a punitive strike to destroy the Black Sea Fleet and its Crimean base at Sebastopol. In other theatres, the Turks fought Russian advances in Armenia, and the British and French sent fleets into the Baltic. There were also minor naval engagements in the White Sea and the north Pacific."