Very many years back my father used to do this work, the job can be very dusty / dirty, the cost then was £££££ Now, I would think it would be around £30 / £50, P/Chimney, there is no other method that can give you the best results, IF there has been a Nest within the chimney, A rod with a large Screw end has to be used to remove, this will be dropped to the Fire Grate, this task can take as long as it takes, & as good as the sweeper Him / her self, the job can be done your self, you can hire the rods, the cover for the front of the fireplace, If you do decide to do the job yourself, make sure ALL AREAS are COVERED BY OLD SHEETS, by not doing this, you will end up getting the whole lot cleaned. Good Luck.