Ok, I don't know the UK healthcare system, but if you have another session write exactly, without metaphor or vitriol, how that encounter with your mother from start to end made you feel and how afterwards your mother made you, a minor she is responsible for, homeless. Tell your therapist in writing how you were harmed and your safety endangered due to their actions. Mail a copy to their main office and to whatever board of ethics or certification is in your area. Keep one for yourself to give to your next therapist. You now have been traumatized by a therapist and the next one(s) need to know what the stakes are when they invalidate your discomfort and condone your mother's neglectful/abusive behavior.

Glad you are headed to a friend's. Stay safe.