Upvote:1
You don't need a plot for casus belli to explain that.
Britain wanted the Ottoman Empire to stand against Russia and was ready to help the Turks. The Turks had low odds against the Russians, so they were ready to put their ships out of Sinope.
British wanted them to stand there because it could have two endings:
Upvote:3
According to the link in the question: "This attack provided France and the United Kingdom with the justification for declaring war on Russia in early 1854 in support of the Ottoman Empire."
Basically, the British ambassador wanted the Turks to lose the battle so that Britain would have an excuse for getting into the war.
At the time, Russia was far stronger than Turkey. Meaning that without British (and French) intervention, the Turks would lose the war, even if they won the battle.
Therefore the Turks "went along" with their allies, because losing the battle would be preferable to losing the war.