Drain cleaning rods, with half moon attachment, use them all the time, just be careful not to be over ambitious and drag too much otherwise it pours over the sides onto the outside of the gutters, the conservatory roof, the old biddy admiring your ingenuity, everywhere.
Also, if you havent already got out get yourself a ladders stand off fro your ladders, it makes everything so much easier if you can actually see what you are doing!!