She didn't cheat on OP as he claims as its obvious they weren't in a committed relationship. However, I can understand how it can be upsetting for the OP having built up a rapport with her through flirting and communications.*
While she's well within her rights to turn him down through her own preference, she didn't handle situation tactfully. In considering they were at least friends, she didn't do the done thing (as most would) and kept her mouth shut about her sexual exploits with the holiday rep bloke.
As a women whom knowingly made it clear to OP that they were nothing more than mates, in the knowledge he fancied the pants off of her, while disclosing to him her conquests, that was cold and heartless.
She should not have done that as a friend, in any case, that's not considering the fact he had romantic intentions and she knew, that is where her contempt lies.
She had a part to play in this situation too, and I think many here are overlooking this, and directing this towards OPs inadequacies or shortcomings. Fact is, she has them too...she coldly decided to (for whatever reason) disclose aspects of her sex life with OP (probably) with the foresight that he'd be upset about that and it would enrage him.
That to me, isn't someone I want to be involved with, romantic or otherwise. She sounds like an immature and emotionally manipulative attention seeker. The worst kind, keeps you there dangling and craves attention to then discard you when someone else that better fits her criteria comes along.
OP it's a lesson to be learned. Find yourself someone whom wants a friendship first and then when that is established build it from there. No need to jump straight to flirtation where a woman can easily string you along as the fairer alluring sex/gender.