You need to take a step back from the rhetoric, and look at the criteria for assessment, which is found in the SEN Code of Practice.
All Local Authorities need to abide by the SEN CoP - they can make their own SA policies, but they can't make policies which take away the rights of parents as provided by the Code.
There are 3 things to consider:
1.Why do you want a statement/Why do you think your DD needs a statement?
2.What do you want the statement to provide?
3.When do you want the statement to be in place?
4.Where do you think your DD needs to be educated?
Firstly, number 4. If you think your DD will or may need a specialist setting, then you will need a statement to achieve that, so appeal will be vital.
Number 2 next. What will a statement provide that is not currently being provided? Apart from the legal clout that a statement gives, the whole point of them is that they are a document which specifies what provision your DD needs which is beyond the resources ordinarily available within the school budget. That can be physical resources, adult support, visits from outside professionals, etc.
Number 3. If the provision in preschool is adequate, then you need a Statement to be in place to provide for her in September. If she needs a specialist setting, you're already running out of time.
The biggy is number 1.
You need to separate out the different issues. The Ed Psych report is a very narrow snapshot of ability. It is largely irrelevant. This is where you need the SEN Code of Practice.
The SEN CoP says:
"4:43 The LEA will then assess the evidence and decide whether the child?s difficulties or developmental delays are likely to be addressed only through a statement of special educational needs. Where a child?s educational needs appear to be sufficiently severe or complex as to require attention for much of the child?s school life, or that the evidence points to the need for specialist early intervention that cannot be provided in the current setting, then the LEA is likely to conclude that an assessment is necessary."
This means that you have to demonstrate that either:
Your DD has severe needs.
OR
Your DD has complex needs.
Complex needs can be relatively moderate needs that overlap and combine to become severe.
For example, my DD was actually quite good with colours, etc., and much of her ed psych report was positive. However, the bits that were negative combined to paint quite a picture. In fact, the ed psych said 'I tried to observe DD from a distance, but this proved impossible.' One of the big things preventing DD1 from being independent is that she has absolutely no 'stranger wariness'. She will walk up to someone, take their hand, and walk off with them, even now at 7 years old.
SO, you may wish to consider whether your DD has needs which are complex rather than severe, looking not only at academic potential but also life-skills.
The next key excerpt from the SEN CoP is:
"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....."
This may be where you fall down. If your DD hasn't had outside support in a setting, then the LA are justified in saying that they want to see how outside support affects the situation.
The best thing to do there, is keep a diary and log any situations where your DD's care at preschool wasn't optimal. Ask the preschool to do the same. Any time there is an incident, all communication difficulties, etc. That way, you can present this as evidence of her need despite intervention.
Then:
"7:14 For some very young children with complex needs the LEA should accept as evidence one over-arching report from the lead professional involved with the child. This approach might also be appropriate for an older child who through an accident or ill health suddenly acquires easily identifiable complex needs that require the LEA to assess and make provision."
You may find that a strongly worded letter from her Lead Consultant stating that she needs a Statement, will be helpful.
Finally, remember that those scores are presumably in 'ideal conditions'. DD's report made much of the fact that while she superficially scored acceptably in ideal conditions, the distractions of a normal classroom would push her scores right down and her attention issues meant she would not cope in a busy environment.
Good luck!