Can the LA refuse to make private provision part of Section F of my child's EHCP when I have evidenced the expertise does not exist locally and that it is required clinically?

My child is unable to eat or drink after suffering trauma at birth. A specialist OT intervention has been requested by his consultant but this is not available in our locality. I have exhausted all other options and found a private provider. The intervention must become an integrated part of my son's care to be successful. It must be carried out at school in the same way as at home so I need it to become part of Section F of the EHCP. The LA have agreed to include some of the advice as part of Section G. My child already has statements on his plan in Section F endorsing the need for consistency, routine and stability in all aspects of his learning. Can I use this as legal grounds to make the private intervention part of Section F?