OP I think you need to take a long, hard look at your readiness to be in another relationship TBH.
If you were with your XP for 4 years and he was EA throughout most of that, your boundaries will have been shot to hell. Getting you to sleep with him after you broke up and when he knew you were in a relationship with someone else, is a natural extension of his control over you (abuse is always about power and control, not anger) and a definite attempt to reassert it, evidenced by the fact he used alcohol to weaken your already low defences and is now threatening to tell.
It's not surprising that you succumbed. It's very common for women in you situation. Don't beat yourself up about that. It just shows you are not free from his abuse yet.
However, regardless of your motives, you now have a DP who has been cheated on. From his POV, the motives are irrelevant because the the end result is the same.
If you genuinely care for him, you have to tell him because he deserves to have the informed choice. Also, telling him removes your XP's power over you. If you are lucky, he may understand what happened, but equally he may not.
You are not a bad person. Most cheaters aren't. They are just people with poor impulse control, poor boundaries or little self awareness. Their behaviour can be very selfish, but it doesn't necessarily follow that they are thoroughly selfish people through and through. I don't think you are. I think you are a woman who ability to maintain her boundaries is damaged. You put up with abuse for a long time. 
In your shoes, I would be tempted to have a period of being single, during which you could get some counselling or learn more about how abusive relationships work. You need to re-establish your inner core and ironically be a bit more selfish when it comes to being assertive and saying "no" when someone puts you in an uncomfortable position. You can do that with a new partner - assuming he's supportive - but it's much easier as a single person.
I hope you manage to do the right thing for all concerned.