Hi, thank you for your question. You are correct in stating that if he has no will, and if you remain unmarried, his estate will automatically be passed down under intestacy rules and therefore to his direct family members (parents - children - siblings etc).
It will be for the person who inherits his estate or property to decide on whether you remain in the property, unless your partner makes a will allowing this. There is no automatic right on you remaining in the property but they should provide you reasonable notice to leave - a year would not be reasonable, but something along the lines of a month would be.
In any event, given that you have cohabited, and if you have done so for 2 years immediately prior to his death and he financially provided for you, you would be entitled to apply to court for reasonable provision from his estate.
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