@PinkPanthreess
I've just read your posts so sorry if I repeat things. And FWIW I'm in the US so some things I say might not apply in the UK
You say he is 'giving his side' to various persons. Do you know specifically what he's saying? There is a big difference between "I hit her, but she drove me to it with her nagging/shouting/bad behaviour" and "She 'came at me' and I defended myself". If it's the former, where he basically admits he struck you even if he says he was 'provoked' which is no excuse, would the people he's telling his lies to be willing to write letters or repeat what they're told to the police? Even though you have the horrific bruises and there is no excuse EVER for physical violence, it might help if there are 'ear witness' statements.
I also agree with a PP that you should ask your SiL to try to get him to leave the home. I doubt it'll work, but what do you have to lose?
In the US if a person reports domestic violence that results in the perpetrator being taken into custody the decision as to prosecute is the District Attorney's, not the victims. The victim can refuse to testify or cooperate, but they don't have to agree with the decision to prosecute.
Again, I'm in the US and I left my husband and the marital home due to his drinking. In actuality I had to be escorted out by the police as he would not let me leave.No violence so he could not be forced to leave. The main thing though is that legally speaking, my being the one to leave had absolutely no effect on my claims on the marital home. This was verified in our financial settlement of 50/50 split when the house gets sold. I also am not required to pay any of those household bills as I was not/am not living there AND I am having to pay for a flat, utilities, etc for my own 'shelter'.
I think at this point, when you're ready, you need to speak to a solicitor. It doesn't mean you have to 'do anything'. It is just to familiarize yourself with what a divorce may mean to you. Take a 'snapshot' of the family finances (both incomes, assets, pensions, mortgage details and show them to the solicitor.
I also believe you should definitely report him to the police, no matter what your sons or your SiL say. Your sons need to understand that there is no excuse for violence and that men who do violence must pay for their crimes. What they are learning now is that "Dad should be allowed to get away with it". That is not a lesson you want them to absorb. If their dad had beaten a man in the street would they say he should get away with that crime? Probably not. Well, there is no difference. But bottom line is, you have the right to make that decision and though I might disagree, I respect that right.
Peace and you are in my prayers.