Cookson announced earlier on Tuesday he would challenge McQuaid for the presidency of cycling's world governing body when the election takes place in September after originally offering his backing to the Irishman earlier in the year.
The UCI was implicated in the Lance Armstrong doping scandal by the US Anti-Doping Agency and was criticised by the World Anti-Doping Agency when an independent panel it established to examine its own alleged complicity was disbanded before it could report.
McQuaid also came in for criticism during the Armstrong allegations and Cookson feels for the sport to finally banish those ongoing problems a change in leader at the top is required.
"I don't want to be too critical of Pat or make this about personalities but clearly we haven't done enough yet to move the situation on from the confessions of Lance Armstrong," he said.
"We need to break out of that era and I believe we need a change of leadership for that to happen.
"I think it is clear that we still haven't dealt satisfactorily with the historic allegations of collusion and intrigue around the lance Armstrong era - we need an independent investigation quickly and I certainly pledge to put that in place as soon as I can if I'm elected.
"I have been on the UCI committee for the last four years and I have inputted as much as I feel I can into that organisation and now it has reached a time when it needs a change in leadership.
"It is mired and tied up in controversies from the past and they always will be until we have that change.
"Things haven't improved or been delivered and I'm convinced that this is the right time for me to put my name forward.
"I'm very, very happy to have an open and constructive debate with Pat or anyone else who wants to be the president."
Cookson, 61, also said he had been asked by people for some time to consider standing for the presidency and has been given support by the likes of Sir Chris Hoy, Chris Boardman and David Millar.
"I have been speaking to people around the world, I have received a good level of indication that there is plenty of support for me," he added.
"It is clear there is an appetite for change out there. I have had hundreds of people emailing me asking what we are going to do about the UCI.
"Until now I have given the same response that we will sit and wait but now we are in a situation where things have not got much better. "I have given my confidence and support to Pat McQuaid until now but we are reaching the deadline for nominations and it is time to put your head above the parapet and that is what I have done."
In the statement made to announce his intention to stand, Cookson made it clear he is keen to build bridges with WADA if his bid for the UCI presidency is successful.
"Cycling is not the only sport with problems but if we don't have a sport that parents can send their children to with absolute confidence then we are failing," he said.
"If elected I will devote myself to rebuilding relations with WADA and establishing with them a completely independent body to deal with anti-doping in cycling so that no-one can doubt that it is being tackled without fear or favour.
"I will also seek their full co-operation in the independent investigation into the UCI's past."
The deadline for prospective presidential candidates to enter the race for September's vote is at the end of the month, with Cookson the only man to so far going public with his intentions.
McQuaid has been president since 2006 but will face a stern test to keep hold of his position given the Armstrong debacle and the threat posed by Cookson.