Yeah, really wouldn't recommend using Adultery - and I say that as someone who actually did have rock solid proof. It presses all the wrong buttons, complicates matters (just saying "he has a partner who stays over" isn't enough - you need something definite and undeniable) and it accomplishes nothing "Unreasonable Behaviour" won't do for a lot less hassle.
I know you said you only started seeing someone in December, however was this a person you'd been emotionally invested in prior to your split? If so, he might being triggered by a primal sense of being replaced. Not saying it excuses his behaviour, however, it might be the sense that this other guy not only caused you to reject him, but now is enjoying the house that was once his, snuggling up on the sofa he once snuggled up on, sleeping on his side of the marital bed, etc, etc... Of course, if he caused the break-up then he doesn't have a leg to stand on and only himself to blame. But, as irrational as it sounds, you being in a new house probably won't be as triggering. Because that won't be his old safe space, place to relax, place he invested in, infused with strong memories of you as a couple.
Whether rightly or wrongly, he's been displace and you haven't. Even if he agreed its for the best, he may still feel it. I felt like this after I separated. I agreed it was best for the kids my wife kept the house. but I still keenly felt that sense I'd lost not only my marriage, but my home, the place I knew, community around me, neighbours and neighbourhood. I felt like Robinson Crusoe.
Again, not that justifies the behaviour. I never told my wife she couldn't have the OP stay over pretty much within days of me moving out, no matter how much it chafed because I knew she was legally absolutely within her rights to do so.