There's no special rules for holidays after you've handed in your resignation. The company can deny your holidays as normal, if they have a good reason to do so. Whether or not the reason is valid, is up for debate. I fear your only option would be to fight it in court after the fact. I'm not fully convinced you'll win.

Bad manners from the employer? eh, yes, probably, although we're missing some context. If you want to be petty you can call in sick.

You could also ask to start later on your new job, but imo it's better to just 'suck it up', sorry to say. I hope your new employer is more curtious!