Contract or similar - death and dividing intestate

[CluelessBananas]

My mum died recently without leaving a will. She didn't leave a huge amount of money, about 15k. My brother and I would like to have a legal document that we can both sign that says we are happy and agree to an equal split and if any further money was discovered through something like premium bonds, this would also be split.

Is there a name for something like this? I have contacted a solicitor but they said we dont need it due to the low amount. However, we would both feel more comfortable with something in place.

You really don't need to put anything in place. You are both entitled to inherit equal shares by law. If anything further is discovered, you will both be entitled to equal shares of that by law. You only need a legal document if you want to do something different.