You say that the school has discriminated against your child. That seems unlikely, unless the admissions criteria have been wrongly applied or are grossly unfair.
What are the admissions criteria for the school? Do they put children in the parish ahead of children outside the parish? Do they put children who attend the parish church ahead of children who attend other churches? If so, that is likely to put you in one of the lower admissions categories and - especially if this is a small school - they are quite likely to have filled all their places with siblings and others in higher admissions categories.
You need to begin by checking
- why you did not get a place (the letter from the LEA should tell you this)
- whether your application was considered correctly - were you placed in the correct admissions category?
If there has been an error which has deprived your child of a place, then (as SchoolsNightmare says) the LEA should give you the place now (although many insist that you go through an appeal anyway). Otherwise, you can appeal. Generally at any admission appeal, parents have to convince the panel that the 'prejudice' (ie disadvantage) to their child in not attending the school is greater than the prejudice to the school in admitting one more pupil.
However, if the school admits in multiples of 30 (ie 15, 30, 45, 60 etc etc) then it would be an infant class size appeal. Because infant classes are limited by law to 30 pupils, the only grounds for winning an ICS appeal are if there has been an error which deprived the child of the place, if the admission arrangements are contrary to law or the admissions code or if the decision to refuse a place was so unreasonable that it cannot be allowed to stand.
If yours is likely to be an ICS appeal, it would be rash to bank on winning it. You may get a place through the waiting list but you need to identify a fallback option (another school or home education).
A lawyer will charge you a lot of money for advice that you can get from Mumsnet!