He's not living there.
He's bullied you into letting him stay for a while, which you did under duress, now you are kicking him out.
The police don't care about whether he lived there anyway, if he's not a tenant legally all they will do is arrest him for breach of the peace if he bangs your door down.
What I've said is straightforward and unfortunately I've got personal experience in it. (thank goodness I turned my life around)
Soon as you can, change locks
get a friend to stay with you perhaps or agree to be on hand when he comes aknocking.
Soon as he refuses to get off your doorstep it's 999 'hello my ex boyfriend is banging my door down while my children are home, they are scared, please come and arrest him'
they will
Go to Women's Aid or phone domestic abuse helpline and ask them to help you get approved for legal aid to apply for a non-molestation order against the man who has been arrested for banging your door down.
Then if he comes anywhere near you he can immediately be arrested.
We hope this gets rid of him but if he does want to take this further you may be eligible to be rehoused.
Don't worry, many of us have been there, don't be ashamed, just course correct.
And don't ever think you need him. He wants you to commit benefit fraud and possibly be imprisoned away from your children, all for his benefit? Absolute scum, and that's without the physical abuse and drinking.