How do I get my ex-partner's belongings out of my house?

If you are the only owner of the house, change the locks again, and if she breaks in again, call the police and have her charged with breaking and entering -- and I'd make sure that she knows you'll do it, if she dares.  The fact that her belongings are inside doesn't give her the right to break into your house if she doesn't live there any more;  if she breaks in and takes anything that isn't hers, it's burglary.

I'm assuming that you were never married, and that there was never any "rent" paid as such, only shared expenses.  So probably your best approach to her belongings would be to rent a storage unit in her name, pay the first month's rent, and put it all there, then send her a certified letter, return receipt requested, telling her what you've done and where she can find her stuff.