it is caused by draughts under the floor rising through the gap under the skirting boards where the floorboards are not sealed to the wall.
You can reduce it by lifting the edge of thee carpet, cleaning the floorboards, and sticking wide tape onto the floorboards and sealing onto the skirting, where it will be hidden by the carpet. You might be able to seal the gap by squirting decorators caulk into the gap under the skirting. You can also put thick paper on the floor so the carpet presses it down. As carpet is porous, the draught blows through it, leaving the dust behind.
My preferred method is to lift the floorboard and pack insulating mineral wool into the gap between the joists, pressed tightly against the wall and the floorboards, but, on the ground floor, not blocking any airbricks (which will usually be lower, anyway). This is rather more work, but can be done if you ever need to lift the floorboards for some other reason.
In UK homes, electrical or heating duct is very rare.