100% it's Bufo bufo, the Common Toad. I don't just think it's fat - I think it has some kind of metabolic problem or an organ issue. Hopefully I'm wrong about that. They are quite capable of climbing but if the wall is sheer then it likely found a way around or under it as the others described.
It should be pretty safe from cats and foxes. It produces distasteful fluid if anything tries to bite it. Things like hedgehogs are more of a danger because they will avoid the skin and just eat the insides. Still, that toad didn't get so big without some good survival skills. I wouldn't worry about it.