If it's not a soul event then of course you have no need to contact the promoter, and the manager should not refuse your business
I am puzzled though.....why would the promoter be bothered about not DJing if it's a birthday party not a soul night?
I'm guessing the music policy was to be Northern, and not general disco/wedding pish?
If so then I still believe the courteous thing to do would to be have approached the promoter first.
It's just general good manners in my opinion, and even though you were not aware of his promotion initially, then you could have followed it up after the manager told you that a soul night already ran in the venue.
Actually why would the manager even mention the soul night if you were booking for a general birthday party.?
Not my venue, not my promotion, not my concern really.......just airing my opinion on how I would have played it.
Best of luck in finding an alternative....I know plenty of suitable venues in the area if you need any info.....Nantwich Civic Hall is a beauty and has 2am license if I remember correctly....Eddie Edmundson ran some hugely successful charity events there a few years back, fantastic dancefloor and has a big car park to rear....plus no soul promotions running from there presently so no grief to worry about!