Not married or in a civil relationship (co-habiting)
If you are not married or in a civil partnership, and you are not named on the property deed or the tenancy agreement, then you do not have a legal right to the property. The person who is named on the deed or tenancy agreement can therefore ask you to leave. However, they should provide you with reasonable notice to do so, but they do not need to.
If you have children, then you should speak to a solicitor for advice if you are not able to agree on custody arrangements.