Why did the british participate in the crimean war?

at first they did not want to allow russians to capture Constantinopol because it would strengthen Russia too much.

In Britain, the Crimean War is principally remembered for three reasons: the Charge of the Light Brigade, maladministration in the British army, and Florence Nightingale. However, this war, fought by an alliance of Britain, France, Turkey and Sardinia against Russia, is far more complex.