OP I am so sorry, but very glad your instinct is to go immediately. You are right. Absolutely right. Note that everyone on here with a similar experience has said just one thing. Wish I'd gone sooner.
I have no direct experience myself but can tell you in a very 'long story short' about an acquaintance of mine who had similar - even down to the gaming. To be brief, she stayed for 2 1/2 years after the birth of their little boy, until he threw the toddler across the room in a fit of anger when he wouldn't stop making a noise. Thank god he landed between a sofa and beanbag and wasn't seriously hurt. He now has supervised access. The rest is a mess.
Someone who can threaten to 'smash your face in' to his pregnant partner over basically nothing isn't in control of themselves, and angry men who can't control an urge to be violent are a danger to everyone but especially babies. Don't take the risk.
To practicalities. Yes, leave, absolutely. You could go to the police and get him out, but for a rented property, it just isn't worth it. You need as little conflict as possible at this stage of your pregnancy and it is 100% easier to safely and quietly arrange to leave while he is out. Fuck the tenancy. The financial side of that can all be sorted with the help of e.g. women's aid as well as the police. To be able to take yourself to a safe location which a. he does not know and b. he has no link or claim to is far safer and easier.
How to do that? Well firstly, do you have family or friends near that you could stay with? If not (and even if you do, this might be preferable) - please consider going to a refuge NEAR to those family or friends and as far as possible from him. Please read the pinned thread on this board on refuges- it sounds a scary option, but really isn't, and would provide a temporary safe place with advice on tap. If you have family you can depend on but don't necessarily want to stay with or who can't put you up, contact them, find a refuge near them, DON'T let him know anything about it and get yourself there. You can stay removed from him for as long as you like. Maternity care can be swapped. If you are then near people you trust, hopefully that will mean a new birth partner too, maybe stay with them straight after the birth. Then you can take it from there.
Once you are out, PLEASE report his threats of violence to the police. This is SO important - as once the baby is born, there will be the question of contact and you need, absolutely NEED to have reported this in order to maintain as much control over initial contact as possible - with this documented, you can push for very little contact at first (as you won't be separated from the baby and if you can eg get a restraining order, you can keep him pretty much away for quite a while). Then you can push for supervised contact etc. Without reporting, this is a LOT harder and you will have a lot less protection from him. Reporting can also make it easier for you to swap maternity care to a new location, get extra support before and after the birth etc. Get the professionals on side - it will put you in control and there won't be a thing he can do to throw his weight around.
Don't have him at the birth - the last thing you need is to feel anxious and stressed in labour.
Don't put him on the birth certificate - he can apply for that later, but again it gives you more control, do NOT give him parental responsibility from the off.
Give the baby YOUR surname.
If you are protected in a refuge, all of this can happen quite safely before he even knows the baby has been born. You could leave a letter advising him that you've left for your own and the baby's safety because of his threats of violence, you have reported to the police and are in a safe location, and you will contact him once the baby is born. Any attempt to contact your family or you will be viewed as harrassment. That's all you need to say. He will then get a visit from the police.
Hopefully this might sound a useful potential way through this. Don't speak to him, contact family/friends and women's aid once he is out of the house and make a list of important documents and sentimental/valuable things to take, but look to getting yourself somewhere where he cannot contact you now for these last few weeks before your baby is safely born.