LGBT advocacy groups have argued that excluding trans athletes amounts to discrimination and that not enough research has been done into the impact of transition on athletic performance.
Others maintain that inherent advantages remain even if testosterone has been reduced.
Fiona McAnena, the director of campaigns at Sex Matters, a women’s rights charity, welcomed Ms Nandy’s acknowledgement that biology matters in sport.
She added: “But the fact that there are 72 trans-identifying male players in women’s football in England alone makes a mockery of the suggestion that most sports are getting their policies right.
“Policies are all over the place from sport to sport, meaning that women and girls face unfairness, the risk of injury and exclusion at all levels.
“Some sports have protected female categories, while others are based on self-identification. There are 18 million women and girls who engage in sport regularly, so this is not a niche issue.
“Fairness in sport urgently needs to be restored for women and girls, and we hope to be among those Lisa Nandy meets to help bring this about.”
Ms Nandy previously prompted a backlash from gender-critical campaigners including JK Rowling, the Harry Potter author, for arguing in 2020 that trans criminals should be allowed to be sent to “a prison of their choosing”.
When she ran for the Labour leadership, she also signed a pledge card that called on candidates to back the expulsion of party members who held “bigoted, transphobic views”.