Dying intestate (without a will) is not good for your family's/loved one's health and sanity!
70% of people die without leaving a will.
To be blunt. If you have are run over by a bus and you have not made a will - where does that leave your family?
They could be left in a nightmare situation, which could take months, even years (in complicated cases) to sort out.
Andrew Way, Partner at Latimer Hinks explains why the Majority of People Risk Leaving Uncertainty Behind
Can I also point you to this blog written about similar problems Wills and Modern Relationships
direct.gov explains What to do if there is no will at all
Whatever the situation it is always advisable to speak to a lawyer.