Who is responsible for the Advisory Teacher? Are they employed by the LA?
In our area, we have the Advisory Teaching Service. They are a department within the LA and come into state schools to provide advice for SEN children. In our area that includes all types of disabilities, including hearing impairments, but not exclusively so.
State schools have to "buy" services from the LA. They get a certain number of credits every year and if they exceed that, they have to buy more or else wait until they are given more credits. It's all part of the state funding package. State schools don't just get it for free.
Private schools don't get any credits so they would have to buy referrals in the same way.
It's the same principle.
The problem is that most private schools won't do this for their pupils. That's the issue here. Many - not all - private schools aren't really that interested in children with SEN or disabilities.