Campbell said: "Chris had been on a short-term contract with us which was due to run out next month. When he received an approach from Orrell to help them out until the end of the season, we felt it was in his interests to allow him to go as quickly as possible. We have been pleased with the progress Chris has made while training with us and playing for GHA in the BT Premiership.
"Having come from the other code, it was always going to take time for him to adapt to the technical side of scrummaging, and he has worked at it well. He is a definite long-term prospect and we will be keeping close tabs on him when he is at Orrell.
"I would like to imagine that some time in the future we would be in a position to renew our links with him."
Before coming to Glasgow in the summer, Scottish-qualified Birchall's only previous union experience was with Otley.
Andrew Plastow, the GHA player-coach, said: "We have been very pleased with Chris's contribution to our campaign this season, and it is disappointing to lose him. Our aim is to get a win against Melrose at The Greenyards this weekend to give him an upbeat send-off."