The corporation had initially retained the comic's Radio 4 series, following the testimony of several women published in The Hollywood Reporter on 1st September, telling British Comedy Guide: "The series is online as part of our archive of radio programming."
However, BCG understands that Contractual Obligation was removed shortly afterwards, in early September.
The BBC's decision follows Veitch being dropped by his US agency, WME, his new comedy special being taken off the HBO Max streaming platform, and his reportedly being edited out of a series he was hosting for short-form streaming service Quibi.
The comedian, who made three series of Contractual Obligation in the last two years, denies the allegations. The women had shared their stories on Facebook, and said they alerted Team Coco, Conan O'Brien's production company, which shot the HBO special.
HBO Max told The Hollywood Reporter: "We were deeply disturbed to learn of these allegations of unacceptable behaviour by James Veitch and will be removing the special from our platform for now."
Team Coco added that they took the allegations "very seriously" and supported HBO Max's decision.
Veitch came to prominence for his shows engaging in correspondence with email scammers, culminating in a 2016 TED Talk that has attracted almost 62 million views.
Last year he hosted BAFTA's prestigious Britannia Awards in Los Angeles. He has deleted his Twitter account since the accusations became public.