By coincidence I was reading an article on school appeals in today's Daily Telegraph. If you really don't feel able to put together an appeal yourself there are a number of companies that exist to do it for you - at a price.
I have no idea how successful or effective they really are - needless to say they all claim fantastic success rates. I would prefer not to post their names here, as I have no way of knowing if they are reputable, but if you Google "School Place Appeal" then some of them appear. You can also read the article at the following link:
However, do read all the advice on the forum first, because it is entirely possible to undertake the process yourself very effectively. There are many people on this forum who are living proof of that. Best of all, the expertise on this forum is completely free.