@Adnerb95
YANBU, what a shit establishment! FFS, they don't allow any margin for error for 8 sodding minutes?! Do they never ever ever have customers coming slightly late, like ever?! Bollocks.
The amount of times I have gone to have my hair done (even a dry cut!) and I have waited 15 to 20 minutes after my appointment time is nobody's business. If I had said 'piss off you're not doing my hair now' to every one, I'd look like fucking Rapunzel now. 
As if they couldn't have given you just a dry cut, or even a wet one.
Shit service. I would never go again. Not sure I would badmouth them online though, as you were the one who was late, but I would take my custom elsewhere, and tell others (verbally,) what happened.
As has been said, they could have fit a dry cut in, and could have made 15 or 20 quid. Clearly they don't give a shit about losing money or custom, as they lost the money you'd have paid for a dry cut AND they will lose you as a customer (probably!)
To the people saying 'she was still 8 minutes late, so it would have thrown the whole appointment system out!' No it wouldn't. They could have still fit her in for a shorter appointment - like a dry cut. No-one can deny that. And it wouldn't have been a 'rush job' if they had had the decency to do a dry cut like the OP requested, because that would have taken less time to do! Is no-one able to work this out?! 
And it's extremely unfair to assume because someone is late one time, that they will always be late. Sometimes things crop up, like traffic jams, late trains and buses, and emergencies, which make people unintentionally late. If it had been the 3rd or 4th time, I would get it, but to 'punish' someone for being a few minutes late ONCE is ludicrous, and is terrible customer service.
Treating customers like this will bite them on the arse eventually.
And I agree that it's bollocks that if they do a wet cut, they need to wait for your hair to be dry to see if they have cut it straight! WTAF?! 
I asked my friend who owns a hair salon what she would do, and she said OF COURSE she would have accommodated the lady, because she cares about her customers, and she cares about her business. Clearly, the salon the OP went to cares about neither one.