Although there are experienced Appeals advisers available for "commercial hire", I would also commend you to our own "Appeals Q&A": http://www.elevenplusexams.co.uk/appeals
The information there may seem overwhelming at first, but it has been carefully compiled by Etienne over more than a decade, and answers many questions that are specific to grammar schools.
It is entirely possible to prepare your own appeal case, at no cost at all, if you take the time to read her advice. She, I and other members are always here to answer questions on the Appeals section if you are struggling with the next steps.
Ultimately, success will depend on the strength of the academic evidence, plus any extenuating circumstances. Whether the adviser is free or charges ££££ is your choice, but we have helped many parents to successful appeals over the years.