When you dive into the world of SEN provision, you will undoubtedly come across a document called the SEN Code of Practice. This is the government document that spells out to schools and LEAs what their duties are regarding special education.
LEAs, under the Education Act "must have regard to" the Code of Practice. For parents, this means that it's a document that you must get to grips with if your child has special educational needs.
For example, the SEN COP says that when a decision is made about whether to make a statutory assessment there is one critical question:
"7:34 In deciding whether to make a statutory assessment, the critical question is whether there is convincing evidence that, despite the school, with the help of external specialists, taking relevant and purposeful action to meet the child's learning difficulties, those difficulties remain or have not been remedied sufficiently and may require the LEA to determine the child's special educational provision. LEAs will need to examine a wide range of evidence. They should consider the school's assessment of the child's needs,including the input of other professionals such as educational psychologists and specialist support teachers, and the action the school has taken to meet those needs. LEAs will always wish to see evidence of, and consider the factors associated with, the child's levels of academic attainment and rate of progress. The additional evidence that authorities should seek and the questions that need to be asked may vary according to the child's age and the nature of the learning difficulty."
Note it does not mention that they need to be so many years behind or that if they are above a certain level then they don't need to be assessed. It is about the child themselves and their progress, rather than where they come on certain scales or test measures. This is particularly true for children with hidden disabilities such as Asperger's or Dyslexia, who are often very bright, but whose achievement could be significantly higher and more in line with their potential if they got the right help.
Also remember that KS1 tests are teacher assessed and may not be an accurate reflection of what your child is achieving. Teachers have been known to misguidedly inflate actual test scores for a child who has a difficulty with recording answers because they know what the child is capable of verbally. But when you come to apply for assessment, the inflated score actually counts against you because although the Year 2 teacher has made an accurate recording of the child's natural ability, it is not an accurate reflection of their achievement.
Download the Code of Practice from the Teachernet website. And then read it and use it to help your child get the help they need. This is, I know, easy to say, because it takes time and energy to get through it and if you're working a long day and dealing with a child with special needs you're probably short on both those things. But the document is fairly well set out, in sub-headed chunks to help you find what is relevant to you. To help, the relevant section for Statutory Assessment is from page 80, or 87/217 on the pdf document.