doesnt sound like a sensor problem if its on all the time, my abs light was on for 4 years and passed mot every time, it wouldn't come on untill the car moved a few hundred yards, so never used to come on going in and out of the workshop, and if it did i blamed the brake rollers confusing the system!
That turned out to be a sensor, unless theres a broken wire somewhere? its a horrible system to try and find issues in!