A child does not need to be 'falling behind' to have a statement. They are for children with physical disabilities too! These extracts are taken from the government guidance on the matter. https://www.gov.uk/government/uploads/s ... carers.pdf
From what you have said it is bizarre that 'they' (who?) have refused to assess him. Either way, I think you need to get the wheels in motion asap to bring your son's physical needs to the attention of the appropriate bod in the admissions authority. Be prepared to spend a couple of days on the phone.
Children and young people with SEN may need extra help because of a range of needs. Paragraphs 6.27 – 6.35 of the 0-25 SEND Code of Practice set out four areas of SEN:
Sensory and/or physical needs – for example, children and young people with visual and/or hearing impairments, or a physical need that means they must have additional ongoing support and equipment.
Many children and young people who have SEN may also have a disability. A disability is described in law (the Equality Act 2010) as ‘a physical or mental impairment which has a long-term (a year or more) and substantial adverse effect on their ability to carry out normal day-to-day activities.’ This includes, for example, sensory impairments such as those that affect sight and hearing, and long-term health conditions such as asthma, diabetes or epilepsy.