If your problem is not p*rn, but your relationship, then this is a different question. But asusming it's not and that you just don't like p*rn, if you've asked them not to look at it, it must be quite a big thing. Regardless of what other people might think on the matter, you are entitled to your opinion on this.
If you have asked your partner not to look at it, I suspect this is because you have a BIG problem. At this point, you are asking someone else to change their life choices because of your views and I hope you have not made this decision lightly.
But if you have thought it through, decided you do have a big problem with it, asked your partner not to, and your partner has agreed to this, him/her going against their word (not sure if your partner is male or female- not that it makes a difference, am just trying to use the right grammar) is an abuse of your trust. The fact that they have tried to hide that fact, means that they know this.
Of course, if partner never actually said they would stop looking at p*rn, then hiding the internet history is them trying to protect you from this issue. And them from the argument.
Either way, I would think the best course of action is to sit down with them and tell them that you know they have looked at p*rn when you have asked them not to, and that you are hurt by this.
If partner had agreed to not look at it, you need t address the issue that perhaps p*rn is a bigger part of his/her life than they first thought when they said they would be fine to go without. Although it could be that perhaps they didn't realise you have as strong feelings about it, as you do. In which case you need to reiterate those.
cont