I have to correct you there, Starsky.
You are right in the fact that the child has a right to contact with a parent, this is now paramount since the Children Act 1989 ~ however the parent does still have the right to contact with the child. In the 'bad old days' children weren't considered with regards to contact.
I also agree with you regarding the costs aspect. If it is Bigapps who has applied for the ammendment, then the cost must be met by them regardless of the outcome.
Luckily when my husband was in this situation he represented himself, so the only cost to him was the application fee.