I would recommend trying to contact either a coach, student, PE teacher or any other teacher from the school you're interested in playing against first, and seeing if they will give you any info.
You could also try writing to the school or emailing them through official channels, although it may take longer to get a reply.
Social media and sites like Meetup.com are also a good way to check out if the school you want to play against has a team. Details of matches may be posted online, and that should lead you to a useful contact.
There are also apps like www.thesupersubapp.com/ which might help find teams to play against in your area, although I have no clue what the app's user coverage is like.