During that massive argument, did you ‘break up’ or discuss breaking up? Did either of you try to reconcile during those two weeks? Moving into the spare room and not speaking for that length of time suggests a serious breakdown in the relationship tbh.
You mentioned he had built up a large deposit—did the topics of moving out, or buying a house come up during that argument? Had he ever mentioned the other woman to you before, even as a friend he was supporting? Or was she a complete surprise?
I’m absolutely playing devil’s advocate here, but—
You accused him of cheating despite never having had reason to suspect him before and it’s possible at that point he wasn’t cheating. The argument was so serious that he moved into the spare room, and (I assume) you didn’t apologise for accusing him. You’d never had a fight like this before. Trust has been broken and he feels you don’t trust him anymore.
At that point, he might have thought: Sod it—I haven’t done anything, but I’m being accused anyway. I’ve spent years saving for a house, but she won’t commit, so where is this relationship going? Then, he turns to the low-hanging fruit—a vulnerable woman he’s befriended. Maybe he confides in her about your relationship breaking down. Suddenly, his ego is being stroked, he’s getting attention he wasn’t getting from you. He has a deposit ready, he knows his housing situation is vulnerable if you kick him out, your relationship is on the rocks/possibly already broken down so he could face being homeless, so he applies for a mortgage (which can be done online in an hour).
Then reality hits. He realises what he’s done but blames it all on you. He’s still angry, nothing has been resolved, and rather than face painful feelings and self-reflection, he runs straight to an OW - something many men do (not as an excuse, just an observation). He feels guilt but also like the victim so he breaks up with you.
This might be completely off the mark, and it doesn’t excuse his actions. He may equally have engineered the breakdown and had an affair. And multiple other affairs, who knows. But to me, it reads as a massive breakdown in communication, leading to the kind of lashing out people do when they’re hurt or feeling like the victim. If any of this rings true, I’d want to hear what he has to say. Not because there’s a way back, and certainly not because what he did was acceptable, but because after ten years, this is such a sad way for things to end. It’s also difficult for your kids to process—someone who was a big part of their lives suddenly gone overnight.