How to navigate the rights of disabled children in mainstream school

Hi Noel
I wonder if you would be able to help me or offer some advice on how to navigate the rights of disabled children in mainstream school, in South London.
My daughter was born with Spastic quadriplegia. She is now 3 and I want her to attend a local primary school with her twin sister. After several visits and meeting to the head teacher (who is very reluctant to accept my daughter into the school) I feel this is the best school for both of my daughters.
The school has wonderful, new facilities, including a lift that would enable my daughter to have access to the building through her primary school years.
The head teacher has repeatedly told me that if she must, my daughter will be able to attend nursery and reception at the school, but then she will need to be separated from her sister from Year 1 and sent to another school. This is not based on my daughter's needs, but simply because the head teacher does not want to change which classes use which classrooms.
I am so angry and confused as to how anyone could be so callous and cruel regarding the needs of a child. My daughter could attend our local special school, but as she has high mental function and I feel she will not be able to achieve her full potential in this setting. The other children have similar physical abilities to my daughter, but she wont have anyone to connect to cognitively.
I am most angry that the school that should be the perfect physical environment for my daughter is denying her access because they do not wish to swap the rooms year 1's are taught in with the rooms the year 4's are taught in. This, to me, seems beyond ridiculous and I cant believe that the head teacher felt it was appropriate to tell me that this was the reason she does not want my child to attend the school.
I just wondered if you could offer me any advice on how to proceed.
Thanks Jane