I would keep music playing in the bird room that covers the majority of the noise. While you won't be able to mask it completely, if there is sound playing almost constantly, the suddenness of a loud noise won't be as bad if Dicky is contently singing away to music.
If possible you could also move the cage as far from the noisy side of the house and keep windows in this room shut during the working hours to cut down the noise.
Will you be at home during the period of time each day when the construction is going on?
I should be home during most of it, obviously I cant guarentee to be here 100% of the time over 5 weeks but I will try my best.
I will get a playlist of his favourite songs while im out (hes very much into rap ) but the fact he nearly has a heart attack every time someone knocks at the door or the window cleaner comes around is worrying me a little.
Also to Therm, thanks a lot, I will try and see if there will be a less noisy area but its a small house and hes currently in one of the furthest away areas.
I might try and get him used to my old mobile phone and actually pop it ontop/next to his cage and play music quietly through that so it seems louder to him without driving me crazy all day.