Tufnell, 48, was eliminated after losing out in the jump against fellow sportsman and former England rugby centre Mike Tindall in Innsbruck, Austria.
While Zara Phillips’ husband, 36, will continue in the show, he told presenter Davina McCall that he was “gutted” to have been forced to jump after losing out in the skeleton to TV personality Louie Spence.
Meanwhile, Parker was knocked out by the former JLS star JB Gill, who currently works as a farmer.
The Gogglebox B&B owner had previously gone up against Jackass daredevil Steve-O in the skeleton.
The posh 49-year-old reality TV star had already been forced to rest last week after suffering a suspected concussion in a crash during training as he tackled a ski cross course.
Thrill-seeker Gill, 28, told presenter Davina McCall: “The first jump is always the hardest so I am glad I have got it under my belt now. I want to go all the way.”
The notoriously dangerous show has already been beset by injuries as celebrities spent the past few weeks developing their skills.
Strictly Come Dancing star Ola Jordan withdrew and had to undergo knee surgery following a fall, and Sally Bercow – wife of House Of Commons speaker John – also had to pull out.
This year’s initial cast of 16 celebrities features the likes of Towie star Joey Essex, entrepreneur Heather Mills, Pussycat Doll Ashley Roberts and former X Factor contestant Stacey Solomon.