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The first chap went up with his iPad and took photos of the chimney, his fingers in the chimney wall where the mortar had fell out, the garden growing behind the chimney and one cracked tile.
He said the ridge tiles were fine and didn't need work. He said he would grind all the old mortar out, blow it with compressed air and repoint; put a new 'top' on the chimney around the chimney pots; put bird guards in the pots; remove the garden and clean the area; clear any mess from the guttering; replace broken tile.
Today's chap didn't go up on the roof at all, said the ridge tiles probably needed rebedding (extra £100) and the felt at the guttering (?) might need doing as well, price not mentioned. I don't trust him to do a proper job. He said he would brush the mortar out.