You have the right to insist that the local education authority conducts a 'special educational needs' assessment. The LEA can only refuse if:
(a) they've conducted an SEN assessment within the past 6 months ; or
(b) if, having examined all of the available evidence, they conclude that an SEN assessment is not necessary.
From your post, it seems extremely unlikely that (a) applies and I can't see how they justify refusal on the grounds of (b).
There's a sample letter for you to modify, and send to the LEA, here:
http://www.dyslexia.uk.com/page79.html
Once a child has been 'statemented' (i.e. a 'statement of special educational needs' has been made) , the LEA is legally obliged to draw up plans to provide appropriate educational facilities and resources for that child.
Forget about battling with the school. It's the LEA which is responsible for assessing your daughter and providing suitable education.
That sample letter is taken from this site:
http://www.dyslexia.uk.com/
Despite the terrible web design, that site contains a great deal of useful information.
Chris
PS: I used to be in teaching and I know that a surprisingly large number of educational problems were eventually traced to medical causes (e.g. sight or hearing problems or dietary problems, e.g. an inability to absorb certain vitamins or minerals). It might be worth having a word with your doctor and getting everything checked out.