It is important for you to realize that you are not the problem. I made this mistake when I found out that my SO was using pornography...we would end up going 7-10 days at a time without being intimate. This wrecked my self esteem for some time. So you will avoid an awful lot of grief by not blaming yourself.
There is no nice way to put this--your boyfriend is a sex addict. This is a very complicated condition and has nothing to do with your body, how you dress, how you look. Most likely, he has had this problem for many years (before you got with him). It probably progressed form 'innocent' porn in his younger years to physical, illicit encounters. Also, there is evidence that these addictions stem from childhood sexual abuse. It is a way to control what he could not control when he was younger.
This is a complicated issue, one that you will probably have to face head-on. Otherwise, it will not resolve on its own. The fact that he is lying about it concerns me. He is heavily entrenched in his addiction and, by doing so, puts you at great risk. The mental and psychological pain is one thing. But, since he is actually having physical relations with other women (you can assume that he is paying the escorts for sex) you are at risk of getting HIV, hepatitis c, or other STDs. This is no joke. I have personally seen someone die from AIDS and it is not fun...his hair was falling out in clumps, he had sores all over his body, he was always getting weird infections, like yeast overgrowth in his mouth.
It is extremely hard to deal with this but you need to set boundaries. Ultimatums may not be effective per se but, unless he gets treatment for this, it will continue to be one vicious cycle. He may tell you he will stop (and he may for a short time). But he will go back to it before you know. This will also affect you and you will have to deal with your hurt feelings. Don't resort to empty threats but follow through. If he continues with the escorts and such, you may need to spend some time apart while you evaluate your relationship. I know it's hard when you love someone but you also have to love yourself. And you have to love him enough to 'push' him in the right direction.
I wish you the best of luck; this is not easy to deal with...just remember that you are not the problem, even if he tells you that you are unattractive or nag too much or whatever.