I doubt that a solicitor would be needed to deal with a slight injustice.
Just possibly for cases involving very complex legal issues (0.1% of appeals at a guess!).
I've never heard an appeal where a solicitor was there with the parents. I've heard a few where the paperwork was written by a professional appeal company including one where they were meant to attend to help out the parents, but dropped out the day before hand! In that particular case, the parents had a good case, but the professional hadn't actually managed to pick it up or put it in the docs - we got it out of the parents ourselves and they won the appeal - despite having paid.
They have all tended to over-egg the pudding, putting too much evidence in about things that really don't make a great deal of difference, but may make the parents think they've got good value.
Apart from the one aforementioned, none have been successful as far as I can remember, purely because the academic ability wasn't strong and the other appeals were more compelling. They also have a tendancy to try & highlight small sections of a school report - we read the whole thing and note that 'Johnny works hard' may be followed by 'for his ability'...
Finally, these are informal tribunals, designed for people to represent themselves. Solicitors are more used to adversorial court proceedings, and not where the 'opposition' may actually be friendly and sympathetic. Panels may well not take well to agressive presentation & questioning - it could sub-conciously affect their view of your case.
However, if you do have a very, very complex legal point, you may want to take advice - but I would say that's more likely to be needed for a permanent exclusion appeal than a grammar admission appeal.