"To get a statement for 'learning difficulties' you have to be in the bottom 1st percentile - and there is no way you'd be in the bottom 1st percentile (cognitively) and 'just' have dyslexia."
Well that is the line parents are fed, indigobell.
DD1 was given a statement at 4.0.
-she had above average colour recognition
-she was toilet trained by day
-she was verbal.
The SEN CoP, coff33pot you can access here then save a copy to your computer. This way, it is fully searchable.
It is why I can give direct quotes - it looks like I've worked hard, but I've actually clicked 'copy' and 'paste' 
The SEN CoP makes NO boundary for SA other than this:
"8:1 Once all the advice requested for the statutory assessment has been received, as described in Chapter Seven, the LEA must decide whether to draw up a statement.
The LEA may decide that the degree of the child?s learning difficulty and the nature of the provision necessary to meet the child?s special educational needs is such as to require the LEA to determine the child?s special educational provision through a statement.
8:2 The LEA will make this decision when it considers that the special educational provision necessary to meet the child?s needs cannot reasonably be provided within the resources normally available to mainstream schools and early education settings55 in the area."
So the criteria is VERY simple.
IF the child has SEN which requires additional resources and the LEA decide that the school the child is assigned to can not 'reasonably' be provided from within the budget of the school, then a Statement should be issued.
It matters not if that child has dyslexia, learning difficulties, ASD, whatever.
However, of course, there are some conditions which are more readily resourced for than others. For example...a child with pure fine motor issues may get a lot of input from OT services, and be given such adaptations as writing blocks, finger supports, etc. It may be that the school can cope very well, so no statement is needed.