Although not currently a way of providing service, attaching a wire to a chimney was allowed in the past and if your service is currently working over it, or could be started in the future over it, as far as Openreach are concerned, until proved differently, the dropwire is ‘good’ and if you want to alter it , for your own reasons ( like working on the chimney) then it would be chargeable work .
If the line in currently in use , your provider would arrange OR to move the line, if not in use then you would approach OR directly, on a forum like this , you would probably only be told the ‘official’ process, obviously, if the line were not in use , you may be tempted to tell the builders to just chop it down themselves, but if it fell into the road and entangled a road user, ( for example ) then the liability for any injury or damage becomes opaque, it wouldn’t be OR responsibility, they never cut it down , and your builder could say they were following your instructions, so personally I would go down the ‘correct’ route.
If the line were chopped without any ‘problem’ , should the line ever be required in the future , charges could apply ( for the obviously damaged dropwire ) and a possible delay , as a new wire wouldn’t simply be put back where the old one was.
