I wouldn’t trust your structural surveyor. It’s visible from here that there are structural issues with that timber frame.I've just been around the house and had another look - the horizontal beam appears to be the width of the wall and is tied to the ceiling beams of the room inside i.e. it's not brick, It appears at some point it's degraded and they've used cement to fill it out in line with the wall. I couldn't see any evidence or movement or damp from the inside (then again I'm not an expert) - but the structural surveyor was comfortable there's nothing of concern structurally with the house (apart from some chimneys requiring reporting) - just that patching up hadn't been done with the correct materials
I would bet my granny’s pension that he is not one of the very few historic specialist surveyors who understand timber frames.
Take a conservation structural framer round on a visit if you are still keen to proceed. They are best places to guide in the extend of work, time, cost and distribution.