Switching my firm to UCL

I’ve recently decided I want to switch my offers and have UCL as my firm instead of KCL. I’ve gotten permission from both Unis and now just need to send a confirming email. My accommodation application has already been submitted through KCL, where I requested intercollegiate halls. I have spoken to the UCL accommodation department and they’ve said that I will have to do a new, late application and be put on a waiting list. I’m concerned that doing this risks not getting a place in halls as I do not want to stay in private accommodation. Does anyone know how likely it would be that a place would become available, or am I better off playing it safe and staying with KCL so that I can definitely stay in halls? I’m very unsure of what to do as I definitely want to go to UCL over KCL but the possibility of not having accommodation is a big worry .