Hi Treacle,
This exact scenario happened to me about 4 years ago.
The Judge, after granting the ICL's request for a family report, instructed both of us that we would be liable for half the cost, to which my ex-wife's duty solicitor responded saying she could not afford it and requested I pay the full amount.
Of course, I refused via my solicitor (was approx $5000 then for 100%) so the Judge told the ex to apply for Legal Aid funding which she did and was granted. Basically, I am trying to say that my understanding is that once the judge orders a Family Report be conducted, then it will happen regardless and someone pays, either the parents or the taxpayer (I could be wrong).
My understanding is that if you claim you cannot pay, you have to be means tested, but as I mentioned, I volunteered for 50% costs so never got to that point.