H & I are separated - not formally. Is there anything (legal) I can do to stop him from letting himself into the house when he pleases?
The house is jointly owned, he says he has the right to be here whenever he pleases. Unfortunately this means that he is now arriving at 6.30am & waking the children. I fear that this will get earlier & earlier.
He's never lived here 'officially', he isn't on the electoral roll for this address.
When you say that he hasn't lived there "officially" do you mean that he doesn't have any possessions at the house?
It's a grey area but some people say that you can change the locks because he no longer lives there. My ex did that when I moved out and I got a letter from her solicitor saying that she'd done it (not that I cared very much). You could add an extra lock to the door and not give him a key. Or tell him that you lost your house keys and had to change the locks, then don't give him a new key.
If he went to court to try and force access they would probably side with you as he doesn't live there and you're entitled to your privacy.