Cox and Britton are inactive for Sunday's game. Both had been listed as questionable.
Will Middleton will start in place of Cox. Veteran Herb Taylor, signed off the street Monday, will start at guard after just three practices - none in full pads. Taylor hasn't played in an NFL game since 2008 with Kansas City.
Jacksonville also will be without running back Rashad Jennings, linebacker Daryl Smith, offensive tackle Cameron Bradfield and defensive ends George Selvie and Austen Lane. They were ruled out Friday.
The Texans will be without receiver DeVier Posey, quarterback John Beck, cornerback Roc Carmichael, cornerback Brandon Harris, linebacker Bryan Braman, offensive tackle Andrew Gardner and guard Brandon Brooks.