I was feeling bad for you as you have only received negative replies. I am no expert on this but Rightmove has a school checker on its website so if you locate a house you can see which schools you are in catchment for. Secondly if you google Bucks County Council Primary School vacancies this lists all schools and what vacancies they have in each year. Obviously this is the current situation and could change daily but may give you an idea of your chances .Good luck .
I would be very
cautious about using rightmove's school checker, having looked at the results for schools around me and knowing what the reality actually is. According to them I'm highly unlikely to get a place at a school I know to be undersubscribed as just one example. I know others have seen similar in other areas. At best it can be used to find what the local schools actually are, but no more. It is probably worse than useless as it is at present.