It also has a lot wider range of industries to protect, so if the UK would be happy in scrapping food subsidies to let African food be competitive in our markets, but other countries like France want to retain subsidies for protectionism of their farmers, it's no dice.

That scenario is exactly what happened in the Doha Development Round.

https://en.wikipedia.org/wiki/Doha_Development_Round

The UE? I see just countries struggling with their own economies, and fighting against UE austerity rules.