TERFing would be terrible but it seems more like Webb is calling out Mermaids (a trans charity who has gotten grants from the British government and prepared educational materials for its school teachers) for making spurious scientific claims and, Webb feels, fast-tracking children who don't want to conform to traditional gender roles into the heavy interventions of medication and surgery. Mermaids got in trouble for this and now the College of GPs and Tavistock (the NHS gender service) are distancing themselves from them, GIDS (the NHS' "Gender Identity Service") dropped Mermaids from their recommended resources, and the Big Lottery Fund is reconsidering its grant.
Webb is basing his concern off the work of journalist Janice Turner, who could well be wrong. I don't know what she found in Mermaids' materials that was so objectionable/false. But if she is refuted I imagine he'd take a different stance, as he holds no truck for traditional notions of "manliness" and gender roles, as someone who is in fact currently on tour for a book he wrote about how much those ideas suck and had a terrible impact on him, and how all masculinity is toxic, called
How Not to Be a Boy. Here is is talking about it:
https://www.facebook.com/watch/?v=2521747174717088