If you die without leaving a will, you are classed as having died 'intestate' so the government is left to decide how best to handle your estate.
If your estate is worth less than £250,000 and one of you dies the other would get all their assets. But if your estate is worth more than £250,000, the first £250,000 would go to the surviving spouse and the remainder would be split in two with half going directly to your children and the other half being put in a trust. The surviving spouse would get a life interest from the trust and upon their death, the money would pass to the children.
If both of you were to die then it would be up to the courts to appoint guardians for your children – and the people you would like to care for them may not necessarily be chosen. Second, your entire estate would be put into a trust for your children, with the trustees, again, chosen by the courts.
If you decide to have a will written, you could consider having 'mirror wills', whereby you both have the same will just with the names reversed. This is cheaper than getting two individual wills as there isn't as much work for a solicitor.