The duo left David Walliams and Simon Cowell on the stage alone after a bust-up over one of the contestants at the Birmingham tryouts.
Comic Walliams tweeted about the incident: "It's all kicked off here in Birmingham for BGT. Amanda & Alesha have staged a walkout. Extremely awkward."
Meanwhile, the official BGT Twitter account confirmed that one act was dividing opinion between the boys and girls on the panel.
The account claimed that a "judge war erupted" over the act.
Audience members tweeted their amazement at Holden and Dixon's actions, commenting: "Omfg, so Amanda and Alesha have walked off stage and not come back for the next act! Too right! #BGT"
Another excited fan wrote: "OMFG AMANDA AND ALESHA JUST HAD AN ARGUMENT WITH SIMON AND DAVID AND WALKED OUT OMFG OMFG OMFG."
Britain's Got Talent returns to ITV in the spring.
Britain's Got Talent 2013 auditions - Photo gallery: