Speaking at a press briefing to announce a new 39-point 'action plan' - a response to the recommendations arising from the ongoing independent review into the culture at British Cycling - Nicholl said that state of affairs was unacceptable.
"I think the revelations yesterday were shocking," she said. "I think the new leadership has to restore the credibility of British Cycling by the actions that they are planning to take."
Browning, who has been in the job for around a month after British Cycling president Bob Howden relinquished his role as chair, agreed. "We absolutely want answers as well over some of the issues flagged by UKAD," he said. "From my point of view, it's not sufficient to be clean, we have to demonstrate that we are clean, transparent in our processes and that's very much include record-keeping in the area of medical support. That's a fundamental responsibility that we take very seriously."
Neither Browning nor Nicholl would comment on the position of Sir Dave Brailsford, Team Sky's principal. Brailsford stepped down as performance director of British Cycling in 2014 to concentrate on his role as the head of Team Sky.
Browning said British Cycling would review its "service level agreements" with Team Sky "and make sure we have a robust process for the avoidance of any conflict of interest. That is something that needs to be managed appropriately."
Nicholl said: "I'm not going to comment on an employee of Team Sky but I would say that, as a result of what I heard yesterday, I'm pleased to hear Jonathan say that British Cycling will take a very close look at the relationship it has with Team Sky, in all matters."
On UK Sport's funding of British Cycling, which was roughly £30million for the last four-year cycle, Nicholl said it would be a "condition of grant" that various reforms were implemented.
"The funding hasn't started flowing yet for Tokyo because the funding for Rio continues up until 31 March," she said. "The funding agreements will be issued in March. But those funding agreements will contain conditions that those action plans that we've talked about and these other commitments that BC is now making will be in there as a condition of grant and there will be timescales."
Wiggins, meanwhile, threatened to call the police after a BBC camera crew tried to speak to him outside his house in Chorley, Lancashire.