The 34-year-old Purkiss, a non-contract player with third-tier Walsall, is keen for the players' union to take on a greater role in helping players with mental health issues.
"I am happy to defend our record – including on issues such as mental health, diversity and player welfare – but I am the first to admit that there are always areas we can improve," Taylor, who has held his role for 37 years, wrote in the letter.
"We owe it to you, our members, to hold ourselves to the highest possible standards... I am adamant that criticism must not be swept under the carpet and instead addressed head on.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"We will be recommending to the PFA's Board of Trustees and Management Committee that an independent QC conducts a full and open review into the structure and operation of the PFA as the trade union for professional footballers in England and Wales."
Taylor did not give details of any other parameters nor the timeline of the review, saying that an update would follow.
"It is important that we are transparent, committed to constantly improving and restless in our mission to support you," the 73-year-old Taylor added.
"I've dedicated the last 40 years of my life to professional football. I am proud of the work we do, supporting our members, whether that's through training and coaching programmes, or promoting diversity and equality in the sport."
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Ken Ferris)
