The problem is, while I don't disagree with the POD suggested, foreign policy is as much pragmatic as ideological. More so the former in many cases. The death of Bismarck, for example, does little to prevent growing tensions between Britain and Russia in Asia. Britain's animosity is going to be focused on, in part, where it perceives the imminent threat.
Moreover, I think people forget just how close Britain and France are geographically. They are natural trading partners. Even at the height of Anglo-French tensions in the nineteenth-century British businesses were investing heavily in France whilst French exports often focused on Britain as a solid market. It is hard to maintain such animosity in the face of such obvious trading connections.
It would also be hard to fulfill, I think, the OC's 200 year scope. I can't think of any nations that have maintained an intense dislike of each other for that period of time in the modern world. Other events always intervene. Take
@CaliGuy 's example of a French victory in the Franco-Prussian War. Yes, it would increase Anglo-French tensions. But has that already failed the criteria given that, in the time between 1815 and 1871 Britain and France have fought a war together as allies against a shared external threat?