Thanks for your question.
My answer assumes that you were not married to the her, are not the father of the children and that you did not agree a fixed term for which she could stay in the property.
If this is the case then she would be regarded as an unlicensed occupier of the property. This means that she does not have many rights. However, one of the rights that she does have is to receive reasonable written notice of eviction.
What is reasonable generally depends on how long a person has occupied the property, but there is not hard a fast way of determining what is fair. However, it is generally thought that two months is sufficicent though it can be less depending on the length of occupation.
Technically, there is no legal requirement for you to apply for a court order for possession of the property once the notice period has expired, but it is generally a good idea since upon eviction it is extremely commonplace for the occupier to either claim physical assault or to claim the notice was not received.
If she has spent substantial monies on the property which has increased the value of the property then this can form the basis of a claim under the trusts of land and appoitionment of trustees act. However, there is no automatic way of claiming the interest - she would have to litigate to claim this and pay legal fees privately.
My goal is to provide you with a good service. If you feel you have received anything less, please reply back as I am happy to address follow-up issues specifically relating to your question.
Kindly rate my answer if you are satisfied with the information I have provided.