Quigg (24-0, 17KOs) was down in the fourth, before the referee stopped it after Quigg landed a body shot in the eighth round.
Quigg was a heavy pre-fight favourite but had problems early in the contest and was knocked to the canvas with a straight left in the fourth.
The Bury-based champion did start getting on top after that and started to dominate in the seventh round.
In the eighth, he caught Arthur (18-6, 4KOs) flush on the solar plexus which caused the challenger to turn around in agony although he didn't fall to canvas.
As Quigg went in for the kill the referee decided to stop the fight and Quigg had made a successful first defence of this title.
Arthur and his camp said they were disappointed with the stoppage and Quigg conceded he was open to the idea of a rematch.
However, there will also be calls for a British super-fight with Carl Frampton, while Quigg has also expressed a desire to fight European champion Kiko Martinez.