The contestants, one of whom is blind and the other of whom is neurodivergent, say they were promised audio descriptions for the questions, which were not delivered.
Both the BBC and the show’s production company, Lifted Entertainment, which is part of ITV Studios, have apologised to the individuals concerned.
One of the affected contestants told BBC News: “One minute before the show, we were told there was no audio description and that your captain will instead have to explain everything.”
These descriptions included visual images including maps and a pie chart, they said, adding: “It was distressing.”
The other contestant 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.
The experience was so “overwhelming and overstimulating”, and that it affected them for weeks afterwards, they said.
The pair – who have asked not to be named – later asked for the episode not to be broadcast, which the BBC agreed to today.
“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 first contestant said.
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.”
Amol Rajan, a former editor of The Independent, took over as the host of University Challenge earlier this year following the departure of Jeremy Paxman after 29 years.
The veteran broadcaster presented his final show in May, two years after he was diagnosed with Parkinson’s disease.