Odd player response to collisions

I have built up a scene from the default "empty room" scene. The bulk of the terrain is flat, but I have laid some "thin" models on the surface (paving slabs & similar - 0.1m high). I've butted several of the model together to form paths.

Now, the default player will wander around this scene and USUALLY happily walks straight onto these slightly raised items. But sometimes collision seems to take effect and he halts. Pressing "jump" gets him up onto the model.

What is even more weired is that sometimes as the player reaches the point where two of these models are butted together, once again he halts (and needs to jump) even though they are the same height.

And I have other objects that are higher (e.g. 0.8m) that he will walk onto without jumping.

I'm sure there must be a rule as to when the player will, or will not, have to jump to get onto these objects, but I've been wandering around the scene for ages & it still seems random to me - I can follow the same path twice & once it needs to jump, the other it doesn't.

Is there some "vertical edge sensitivity" that can be set (i.e. a height above which the player has to jump to proceed)? Am I missing some attriute on the models that might influence this? (I thought I'd given all the models fundamentally the same settings, but maybe I have missed something)