I am assuming you do not need to get probate because her assets are very minimal or all assets pass by survivorship.
Your next steps depend on whether she left a will or not and whether you are the executor/entitled personal representative. If you are the executor (or if not, you are the person entitled to her estate under intestacy), you do the following:-
1) register the death. you will be provided with two types of certificate - one is the standard death cert, the other will need to be sent to the DWP so they can deal with outstanding pension details
2) organise the funeral
3) send original copies (I know that sounds daft but I mean originals from the registrar) of the death cert to the asset holder and ascertain the balances due asking them to remit the balances to you and explaining that as the administrator under intestacy you are intending to adminster the estate under the Administration of Estates (Small Payments) Act 1965.
4) ascertain the debts owing
5) apply the assets collected against any debts and funeral account
6) distribute the remainder according to the will/intestacy rules
Depending on your mother's circumstances, you may also need to contact the tax office to check her tax affairs are up to date.