On Thursday, Banijay UK said Wallace would step away from presenting the show while allegations of historical misconduct were investigated.
He is “committed to fully co-operating throughout the process”, Banijay added.
It came after BBC News sent a letter to Wallace’s representatives, setting out allegations we have heard from 13 people, across a 17-year period.
One of them was broadcaster Kirsty Wark, a Celebrity MasterChef contestant in 2011, who said he told “sexualised” jokes during filming.
It comes as broadcasters and production companies face fresh questions over their handling of allegations against Wallace.
Radio host Aasmah Mir said she initially complained to Banijay in 2017 about inappropriate comments Wallace had allegedly made during filming of the programme. It is believed she then had to take her complaint to the BBC.
In an internal email, BBC executive Kate Phillips, who now heads up unscripted programmes for the corporation, said his behaviour on set was “unacceptable and cannot continue,” the Sunday Times reported.
She added she would make sure that she was “informed straight away” should further allegations be made against him.
Mir later sent an email that was copied to Phillips, saying: “This must not happen again to another woman.”
Some of the allegations against Wallace in the BBC News investigation relate to events after 2017.
There was another complaint in 2018, which our investigation revealed, relating to a different show called Impossible Celebrities.
A BBC probe at the time found his behaviour was “unacceptable and unprofessional” and he got a 90-minute talking to by Ms Phillips.
Separately, the Observer says a letter containing multiple claims of inappropriate behaviour by Gregg Wallace was sent to the BBC in 2022, but did not result in further investigation at the time.
A BBC source said on Sunday “it would be wrong to report the BBC has done nothing if or when matters have been raised with us”.
“We continue to urge caution about pre-judging any of this, particularly the involvement of BBC staff members and any inference they have not acted appropriately,” the source told BBC News.
On Saturday, Banijay UK announced it had appointed “rigorous” law firm Lewis Silkin to lead an investigation into Wallace’s alleged misconduct.