Assuming you have no children of the relationship, and assuming that she pays no rent, then she is simply an unwelcome guest and you would be at liberty to simply lock her out.
She has no financial interest in the property, no legal interest because she is not on the title deeds, and no tenancy.
She has no more right to stay in the property than I do, the postman does, or the milk or the next door neighbour.
Indeed, even if she paid rent she is only a lodger and you could exclude her from the property on one months notice.
I will explain a little more
Provided she shares some facilities, kitchen, bathroom, lounge, whatever, and his accommodation is not self-contained, then you do not need a court order to get her out and when the notice has expired, you can simply lock her out provided you give erm her belongings back.
Here it is from the government website.
However in your situation she doesn’t even pay rent so when she goes out to the shops one day, but all her belongings on the doorstep and change the locks. If she starts to be awkward, call the police.
She clearly does have somewhere to go because she lived somewhere before she moved in a few weeks ago.
You might want to show her this answer and tell her that one day she is going to come back and find the locks changed.
Thank you for letting me assist you with your legal question. I am glad that I was able to help.
I am not certain whether that answers the question for you or not, but I am happy to answer any specific points arising from this.
It will be my pleasure to help you again either further with this or any future questions you have