I'm so sorry, OP.
As a PP said, what you need to decide for yourself is not if he is lying or telling the truth, but if you can trust him, if you can live with even the possibility that he has paid for sex/thought about paying for sex.
You say he has "form" for stupid little lies, and little lies often lead to bigger ones.
If I were you I'd divorce, because it sounds as if you are a parenting solo anyway most of the time if he works away, and so practically life will be no worse without him permanently.
It is very easy to sit behind a screen and say "I would do this" or LTB immediately but harder in real life.
Think it over but consider that the most probable explanation is that he did it, not his "mate". And that regardless, he thought it was OK to treat you so disrespectfully as to fail to discuss it immediately you found it. He didn't care how you were feeling. He didn't care about you.
He will beg you so as not to lose face, so his family and friends don't discover his grubby actions. That's a given. But can you really truly hand on your heart say he's begging for your forgiveness and trust because he live you more than anything? That's what you need to ask yourself.
At this point it is about you, not about him. Focus on yourself.