She could pay for a private Ed psych assessment.
She could also call the school and make an appointment to discuss with the senco. Or call the lea and discuss what the school have said regarding assessment with the area inco.
To be frank though, she will need to have documented this through time, and be able to prove that the school has been providing support which is inadequate.
Se needs to know if the dd has been on the 'school action' list. If so, how long for.
She needs to know if IEPs have been in place for the child (she should have an entire folder of copies of them if this has been ongoing for years - they should be updated six monthly once out of yr r, and parents should be signing).
In any case, I would be booking an appointment with the senco to discuss transition to secondary.
It's hard when kids are borderline though. The truth is, there is very little support for kids who are slower to pick up concepts (we aren't all going to be Einstein) but not academically behind enough to be assessed for any learning disabilities.
At 10, they probably see no point in starting the assessment wheel turning - she will be in a different school by the time/ if ever she reaches the top of the waiting list.
Can they afford a private Ed psych assessment?