I think you have misread the Times article.
It is the gender-critical Stephanie Davies-Arai, director of Transgender Trend, not trans rights groups, who has said that the proposals risked having a “chilling effect” on free speech.
It actually says that trans rights groups said that there would be 'a “chilling effect” on free speech':
Government sources suggested that organisations such as Mermaids, a charity that offers advice and counselling to children with gender dysphoria, could be outlawed. Trans rights groups said that the proposals risked having a “chilling effect” on free speech.
It uses the phrase "chilling effect" again later when talking about Transgender Trend (but not in relation to free speech):
Stephanie Davies-Arai, director of Transgender Trend, a group of parents, professionals and academics troubled by the trend to diagnose children as transgender, said that the new laws could threaten legitimate discussions.
She said: “This may have a chilling effect on therapists working with children with gender dysphoria unless there are clear, specific protections built into the bill.”
But who knows who actually said what in such a garbled article.