The contestants said that there was a lack of provision for their disabilities whilst filming the festive episode of the BBC quiz show.
One contestant, who is blind, explained that they had been caused distress after the audio description that they had been promised was not provided to them.
Meanwhile, a neurodivergent contestant’s request for subtitles is understood to have been turned down.
The BBC has since issued an apology to the contestants involved, while production company Lifted Entertainment offered its “sincere apologies”.
According to the BBC, the two contestants, who wish to remain anonymous flagged their disabilities to the producers before the recording but they were not properly accommodated.
One contestant said: “One minute before the show, we were told there was no audio description and that your captain will instead have to explain everything.”
They went on to explain that several visual images, including a pie chart and maps, needed to be described, adding: “It was distressing.”
The other contestant, who has challenges with audio processing, said they had requested subtitles in advance so they wouldn’t be at a disadvantage.
“Unfortunately, I was told this wasn’t possible,” they said, before revealing that other requests to help manage their sensory needs were not met.
They also said that the lack of provisions had meant that the experience was “overwhelming and overstimulating” – so much so that their ability to function was affected for one week following filming.
Following their upsetting experience, the contestants issued a complaint to the BBC and asked that their episode not be broadcast, with one saying: “I was in touch to say I’d prefer not to have the manifestation of my disability broadcast on network TV in the run-up to Christmas.”
The episode of Christmas University Challenge, which is a festive spin-off from the BBC Two show, was axed on Friday.
Both contestants voiced their gratitude over the decision to pull the episode and have since offered to help showrunners make the programme more accessible.
A BBC spokesperson said: “We can confirm that an episode in the upcoming series of Alumni University Challenge will not be broadcast because two of the contestants felt their access requirements were not sufficiently met by the production.
“We are working closely with producers to improve cross industry access on our programmes to ensure a consistent approach is implemented.
“We would like to apologise to the individuals and teams concerned, and they have been written to personally by the producers.”
Lifted Entertainment said: “During the pre-filming briefing for this episode, two contestants requested that certain adjustments be made in order for them to be able to fully participate.
“However, following the recording, we were made aware that the adjustments made fell short of their requirements. We have spoken to the individuals involved and offered our sincere apologies.
“Having listened very carefully to their descriptions of their experiences, we agreed with the BBC that the fairest course of action was not to screen this particular edition.”
The remaining episodes of the Christmas spin-off, which are presented by Amol Rajan, are said to have not been affected by this decision.