The 32-year-old prop had decided to rejoin Rotherham on loan last week and was set to debut against the Championship's bottom club in the rearranged game tomorrow.
However, he has gone back on the decision and signed for Premiership leaders Northampton Saints instead, much to the disappointment of the Titans staff.
Titans head coach Andre Bester, who will be now forced back into the transfer market to strengthen his front row, said: "We had done a deal and Ben was looking forward to coming back here but then Northampton offered him a deal.
"He took it and while we are disappointed, it's not the end of the world.
"We will keep looking and we have people out there searching for the right man. We won't make any signings until we get the right man."
Rotherham's trip to Birmingham was originally scheduled for Boxing Day but due to the wintry weather, a decision was taken last week to postpone it by another 48 hours.
A statement from the Bees read: "By moving the game now to the Bank Holiday Tuesday, we give ourselves two extra days for the weather to improve, whilst also giving supporters, players and staff from both clubs as much notice as possible to reshape their plans over the festive period.
"There will be a pitch inspection on Monday ahead of the rescheduled game."
All tickets for the game, which will kick-off at 3pm, are still valid.