Hello Louise
Your H reminds me very much of my ex. Fun, kind, generous, charming. Also weak, deceptive, secretive and rather pathetic.
He thrived on collecting women, flirtation, many secret rendezvous for no-strings sex, and an addiction to porn. Towards the end of our five year relationship he was physically incapable of sex too - with me. It just didn't excite him enough, the way the secret relationships with others did.
He had two or three phones, several email addresses and was listed on many internet dating sites. He lived his "real" and secret life in his head, online, and through quick casual meetings with women.
I understand that you want solid proof to confront him with. You will, as I did, struggle to get this, as you know he is good at hiding evidence, even if he's not that adept at completely covering his tracks. All you really need to confront him is your deep unhappiness and distrust.
Yes, he will tell you you're the architect of your own misery and the fault lies with you in creating distrust within the relationship. But you, and he, know that's not the case. Unless he is prepared to do ANYTHING to repair your lack of trust in him, you are on a hiding to nothing here, and so is he. He can rationalise your suspicions and unhappiness as much as he wants, but that doesn't take them away. Unless he can provide you with proof that he isn't having inappropriate relationships with other women, your fear and lack of trust will remain. And don't let him fob you off with spurious ideas of his "right to privacy" either. He needs to figure our what's more important to him. Refusing to give you passwords is a dead giveaway.
With my ex, my trust was so damaged nothing he could have done would have made everything alright again. I knew he would find ways to continue to cheat, no matter how convoluted they became. Without trust you are doomed to a miserable life.
I'm so sorry you're going through it. I remember the pain very keenly.