The pair travelled to the bridge last Wednesday, breaching security, before scaling one of the bridge's giant cables, hundreds of feet above traffic, wearing Go Pro action cameras, but no safety gear.
But they turned back a short distance from the top after security cameras spotted them.
They were spoken to by police, later telling viewers, who have seen the video online more than 458,000 times: "They can't prosecute us - they asked up to wipe the footage."
Dave Roberts, coxswain of the inshore lifeboat Humber Rescue, blasted the "mindless idiots", adding: "One does it and they are all at it like lemmings. They want to see the consequences (of someone falling). It's not a pretty sight."
A spokesman for the Humber Bridge criticised the copycat attempt, which followed one by the four-strong Night Scape group from London in May.
The bridge spokesman added: “We will be pursuing a private prosecution against the individuals involved for breach of our byelaws, which prohibit people from climbing the Humber Bridge in this manner.
“After climbers reached the top of the Humber Bridge in May, we announced a review of security around the access points to the cables.
"Work has been ongoing since that time to ensure gaining unauthorised access to the cables is much more difficult than it used to be.
“When the latest breach occurred on Wednesday, this work had been completed on three out of the four access points.
"The climbers choose the only access point that had yet to be updated. Work was completed to update the final access point on Friday.
“We’re very confident that the security around the access points will prevent the vast majority of people from accessing the cables.
"However, we have always maintained that it would be impossible to stop absolutely everyone. Experienced climbers, who have no regard for their own safety and that of others, and who are determined to reach the top, will try to bypass whatever security is in place."