If he loves you and wants it to work, he will do everything you ask of him, everything you need to help you to move on.
It's simply not good enough of him to expect you to just forget about it because he says so. He's already blaming you for it, when it's actually HIS fault and something he needs to take responsibility for.
And, sorry, but ime they will admit as little as they possibly can
"I didn't do ANYTHING"
"well, ok, since you've got the phone bill, I admit I spoke to her, but nothing else, I swear in the kids lives"
"Ah, you've found the hotel bill, well, ok, we shared a room that one night the bill is for - but I swear on the kids lives we didn't sleep together"
"oh, you've found the empty condom wrapper. Well, ok, we slept together once, - how many wrappers did you find? yes, just the once and I didn't enjoy it, in fact she MADE me do it, I was thinking of you the whole time"
"oh, you hired someone to follow me and you've got pictures, well, she trapped me into it, I have been going crazy with the guilt, it never would have happened if you'd had sex more/looked better/lost weight/paid more attention to me"
etc
etc
etc
If he won't cut contact, be honest and go to relate with you - he just doesn't care enough and isn't worth it.