My son is 9 and attends a special school not far from you although in a different borough. Your dd sounds very similar to him, he is totally non verbal also. He started nursery at his special school (is still there now) and even though we have issues sometimes it absolutely was the right decision for him. I viewed both mainstream and special schools and asked lots and lots of questions. It was clear when i viewed the mainstream schools they would have no clue how to help him, nor did they have the resources. It is very important that you see both and follow your instincts. Only you know your dd and what she needs.
Most special schools have there own speech and language therapist, this may be attractive as nhs salt can be a challenge at times. This is not a statutory service but many do provide this.
Consider what communication aid your dd uses, can the school meet these needs. If in mainstream would she have a 1:1 who understood pecs or proloquo2go as an example (depending on what she needs).
Can the environment meet her sensory needs, do they have understanding of this? Do they have a sensory safe space/room?
Does she require ot? Some special schools have there own on site, my sons does.
Class size? Would she benefit from a smaller class with higher staffing ratio? Would she cope in a class of 30?
I would go and see as many as you can because provision really does vary even between special schools.
Hope this helps and good luck!