he only did it because he has been feeling lonely and feels that I am a million miles away
Aw you were neglecting him, you were unavailable, distant, not connecting ... It's actually your fault/failing.
Because if you're a decent faithful partner to someone, you don't talk to them about it and try to resolve it repeatedly, and if it doesn't get resolved with peserverence/ several attempts .. separate from them.
No, you don't do that, instead as a reasonable, decent, committed, faithful partner; you register on dating sites and communicate with people looking to meet someone for anything from sex to a relationship and make arrangements to meet them.
Are you also allowed to go in dating sites, chat to other men, and make arrangements to meet them (if you're feeling he's distant obviously)?
Op I'm really sorry but I think that if he hadn't actually/truly cheated already, he seems the type of person to do so sooner or later, he'll.just hide it better next time (after lying low for a while).
Plus he's a c*nt for messing people who.are genuinely looking for a partner. At best he's wasting their time and taking the piss out of them. At worst he's dra omg them i.to a cheating situation that they're probably unaware of, he's probably presented himself as single.