NotSpaghetti
Is it a pointing problem?
It looks as though soot is somehow seeping through below the redder bricks.
I too thought the pointing is eroded in the top part of the chimney, in the section between the two bands of contrasting bricks. Perhaps that section has been rebuild by other hands (less skilled) that the rest of the chimney? The chimney lining may be faulty there, and if there is no ventilation there could be condensation where the chimney is colder above the roof. That would make it vulnerable to dirt and to mould growth. A chimney sweep or a builder would be able to advise you. it doesn't look very sound, though. The surveyor sounds a bit vague. You do wonder what you are paying for - they even have a disclaimer saying (in effect) that if they miss something important they are not to be blamed.
